Final Test Bank Chapter 10 Rotation - Fundamentals of Physics 11e Complete Test Bank by David Halliday. DOCX document preview.
Chapter: Chapter 10
Learning Objectives
LO 10.1.0 Solve problems related to rotational variables
LO 10.1.1 Identify that if all parts of a body rotate around a fixed axis locked together, the body is a rigid body. (This chapter is about the motion of such bodies.)
LO 10.1.2 Identify that the angular position of a rotating rigid body is the angle that an internal reference line makes with a fixed, external reference line.
LO 10.1.3 Apply the relationship between angular displacement and the initial and final angular positions.
LO 10.1.4 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
LO 10.1.5 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for that change.
LO 10.1.6 Identify that counterclockwise motion is in the positive direction and clockwise motion is in the negative direction.
LO 10.1.7 Given angular position as a function of time, calculate the instantaneous angular velocity at any particular time and the average angular velocity between any two particular times.
LO 10.1.8 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time and the average angular velocity between any two particular times.
LO 10.1.9 Identify instantaneous angular speed as the magnitude of the instantaneous angular velocity.
LO 10.1.10 Given angular velocity as a function of time, calculate the instantaneous angular acceleration at any particular time and the average angular acceleration between any two particular times.
LO 10.1.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between any two particular times.
LO 10.1.12 Calculate a body’s change in angular velocity by integrating its angular acceleration function with respect to time.
LO 10.1.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
LO 10.2.0 Solve problems related to rotation with constant angular acceleration
LO 10.2.1 For constant angular acceleration, apply the relationships between angular position, angular displacement, angular velocity, angular acceleration, and elapsed time (Table 10.1).
LO 10.3.0 Solve problems related to relating the linear and angular variables
LO 10.3.1 For a rigid body rotating about a fixed axis, relate the angular variables of the body (angular position, angular velocity, and angular acceleration) and the linear variables of a particle on the body (position, velocity, and acceleration) at any given radius.
LO 10.3.2 Distinguish between tangential acceleration and radial acceleration.
LO 10.4.0 Solve problems related to kinetic energy of rotation
LO 10.4.1 Calculate the rotational inertia of a single particle moving in a circle, as measured relative to the center of that circle.
LO 10.4.2 Find the total rotational inertia of many particles moving around the same center.
LO 10.4.3 Calculate the rotational kinetic energy of a body in terms of its rotational inertia and its angular speed.
LO 10.5.0 Solve problems related to calculating the rotational inertia
LO 10.5.1 Determine the rotational inertia of a body if it is given in Table 10-2.
LO 10.5.2 Calculate the rotational inertia of a body by integration over the mass elements of the body.
LO 10.5.3 Apply the parallel-axis theorem for a rotation axis that is displaced from a parallel axis through the center of mass of a body.
LO 10.6.0 Solve problems related to torque
LO 10.6.1 Identify that a torque on a body involves a force and a position vector, which extends from a rotation axis to the point where the force is applied.
LO 10.6.2 Calculate the torque by using (a) the angle between the position vector and the force vector, (b) the line of action and the moment arm of the force, and (c) the force component perpendicular to the position vector.
LO 10.6.3 Identify that a rotation axis must always be specified to calculate a torque.
LO 10.6.4 Identify that a torque is assigned a positive or negative sign depending on the direction it tends to make the body rotate about a specified rotation axis: “clocks are negative.”
LO 10.6.5 When more than one torque acts on a body about a rotation axis, calculate the net torque.
LO 10.7.0 Solve problems related to Newton's second law for rotation
LO 10.7.1 Apply Newton’s second law for rotation to relate the net torque on a body to the body’s rotational inertia and rotational acceleration, all calculated relative to a specified rotation axis.
LO 10.8.0 Solve problems related to work and rotational kinetic energy
LO 10.8.1 Calculate the work done by a torque acting on a rotating body by integrating the torque with respect to the angle of rotation.
LO 10.8.2 Apply the work–kinetic energy theorem to relate the work done by a torque to the resulting change in the rotational kinetic energy of the body.
LO 10.8.3 Calculate the work done by a constant torque by relating the work to the angle through which the body rotates.
LO 10.8.4 Calculate the power of a torque by finding the rate at which work is done.
LO 10.8.5 Calculate the power of a torque at any given instant by relating it to the torque and the angular velocity at that instant.
Multiple Choice
1. A radian is about:
A) 25
B) 37
C) 45
D) 57
E) 90
Difficulty: E
Section: 10-1
Learning Objective 10.1.0
2. One revolution is the same as:
A) 1 rad
B) 57 rad
C) /2 rad
D) rad
E) 2 rad
Difficulty: E
Section: 10-1
Learning Objective 10.1.0
3. One revolution per minute is about:
A) 0.0524 rad/s
B) 0.105 rad/s
C) 0.95 rad/s
D) 1.57 rad/s
E) 6.28 rad/s
Difficulty: E
Section: 10-1
Learning Objective 10.1.0
4. If a wheel turns with constant angular speed then:
A) each point on its rim moves with constant velocity
B) each point on its rim moves with constant acceleration
C) the wheel turns through equal angles in equal times
D) the angle through which the wheel turns in each second increases as time goes on
E) the angle through which the wheel turns in each second decreases as time goes on
Difficulty: E
Section: 10-1
Learning Objective 10.1.1
5. One-dimensional linear position is measured along a line, from a point designated x = 0. One-dimensional angular position:
A) is measured along a line, from a point designated θ = 0.
B) is measured along the axis of rotation.
C) is the angle that an internal reference line makes with a fixed external reference line.
D) is measured relative to the positive y axis.
E) is meaningless, as rotations take place in two dimensions.
Difficulty: E
Section: 10-1
Learning Objective 10.1.2
6. An object rotates from θ1 to θ2 through an angle that is less than 2π radians. Which of the following represents its angular displacement?
A) θ1
B) θ2
C) θ1 - θ2
D) θ2 - θ1
E) θ1 + θ2
Difficulty: E
Section: 10-1
Learning Objective 10.1.3
7. If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:
A) 0.33 s
B) 0.67 s
C) 1.0 s
D) 1.3 s
E) 2.1 s
Difficulty: E
Section: 10-1
Learning Objective 10.1.4
8. If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:
A) 0.31 rad/s
B) 0.63 rad/s
C) 10 rad/s
D) 31 rad/s
E) 63 rad/s
Difficulty: E
Section: 10-1
Learning Objective 10.1.4
9. The angular speed of the second hand of a watch is:
A) (/1800) rad/s
B) (/60) rad/s
C) (/30) rad/s
D) (2) rad/s
E) (60) rad/s
Difficulty: E
Section: 10-1
Learning Objective 10.1.4
10. The angular speed of the minute hand of a watch is:
A) (60/) rad/s
B) (1800/) rad/s
C) () rad/s
D) (/1800) rad/s
E) (/60) rad/s
Difficulty: E
Section: 10-1
Learning Objective 10.1.4
11. A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves is:
A) 50 rad
B) 75 rad
C) 150 rad
D) 314 rad
E) none of these
Difficulty: E
Section: 10-1
Learning Objective 10.1.4
12. Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is:
A) 3.14 rad/s2
B) 30 rad/s2
C) 30 rev/s2
D) 50 rev/min2
E) 1800 rev/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
13. A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration of the wheel during this process is:
A) 1/ rad/s2
B) 2 rad/s2
C) 4 rad/s2
D) 4 rad/s2
E) 72 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
14. A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration for this process is:
A) 1.5 rad/s2
B) 1.5 rad/s2
C) /40 rad/s2
D) /20 rad/s2
E) 0.75 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
15. If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:
A) clockwise about an axis that is perpendicular to the page
B) counterclockwise about an axis that is perpendicular to the page
C) about an axis that is parallel to the page
D) about an axis that is changing orientation
E) about an axis that is getting longer
Difficulty: E
Section: 10-1
Learning Objective 10.1.0
16. The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:
A) the body is slowing down
B) the body is speeding up
C) the body is starting to turn in the opposite direction
D) the axis of rotation is changing orientation
E) none of the above
Difficulty: E
Section: 10-1
Learning Objective 10.1.0
17. The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration of this wheel is:
A) 42 rad/s2
B) 2 rad/s2
C) 1/30 rad/s2
D) 2/30 rad/s2
E) 4 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
18. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?
A) 3.0 s
B) 6.0 s
C) 9.0 s
D) 18 s
E) 36 s
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
19. A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is:
A) 2.0 rad/s2
B) –2.0 rad/s2
C) 3.0 rad/s2
D) –3.0 rad/s2
E) 6.0 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
20. A wheel initially has an angular velocity of –36 rad/s but after 6.0 s its angular velocity is –24 rad/s. If its angular acceleration is constant the value is:
A) 2.0 rad/s2
B) –2.0 rad/s2
C) 3.0 rad/s2
D) –3.0 rad/s2
E) –6.0 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.5
21. The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:
A) 
B) 
C)
D)
E)
Difficulty: M
Section: 10-1
Learning Objective 10.1.0
22. An object rotates from θ1 to θ2 through an angle that is less than π radians. Which of the following results in a positive angular displacement?
A) θ1 = 45°, θ2= −45°
B) θ1 = 45°, θ2= 15°
C) θ1 = 45°, θ2= −45°
D) θ1 = 135°, θ2= −135°
E) θ1 = −135°, θ2= 135°
Difficulty: E
Section: 10-1
Learning Objective 10.1.6
23. The coordinate of an object is given as a function of time by θ = 7t – 3t2, where θ is in radians and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:
A) 5 rad/s
B) –5 rad/s
C) 11 rad/s
D) –11 rad/s
E) 1 rad/s
Difficulty: M
Section: 10-1
Learning Objective 10.1.7
24. The coordinate of an object is given as a function of time by θ = 7t – 3t2, where θ is in radians and t is in seconds. Its angular velocity at t = 3 s is:
A) −11 rad/s
B) −3.7 rad/s
C) 1.0 rad/s
D) 3.7 rad/s
E) 11 rad/s
Difficulty: E
Section: 10-1
Learning Objective 10.1.7
25. This graph shows the angular position of an object as a function of time. What is its average angular velocity between t = 5 s and t = 9 s?
A) 3 rad/s
B) −3 rad/s
C) 12 rad/s
D) −12 rad/s
E) Need additional information.
Difficulty: E
Section: 10-1
Learning Objective 10.1.8
26. This graph shows the angular position of an object as a function of time. What is its instantaneous angular velocity at t = 1.5 s?
A) −6 rad/s
B) 6 rad/s
C) 9 rad/s
D) 12 rad/s
E) Need additional information.
Difficulty: E
Section: 10-1
Learning Objective 10.1.8
27. Instantaneous angular speed is:
A) total angular displacement divided by time
B) the integral of the displacement over time
C) the rate at which the angular acceleration is changing
D) the magnitude of the instantaneous angular velocity
E) a vector directed along the axis of rotation
Difficulty: E
Section: 10-1
Learning Objective 10.1.9
28. The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t – 2.7t2. What is its angular acceleration at t = 2.0 s?
A) −10 rad/s2
B) –5.0 rad/s2
C) −5.4 rad/s2
D) 2.4 rad/s2
E) 3.1 rad/s2
Difficulty: E
Section: 10-1
Learning Objective 10.1.10
29. The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t – 2.7t2. What is its average angular acceleration between t = 1.0 s and t = 3.0 s?
A) 0.64 rad/s2
B) −5.4 rad/s2
C) −7.7 rad/s2
D) −10 rad/s2
E) −27 rad/s2
Difficulty: M
Section: 10-1
Learning Objective 10.1.10
30. This graph shows the angular velocity of a turntable as a function of time. What is its angular acceleration at t = 3.5 s?
A) −10 rad/s2
B) −5 rad/s2
C) 0 rad/s2
D) 5 rad/s2
E) 10 rad/s2
Difficulty: E
Section: 10.1
Learning Objective 10.1.11
31. This graph shows the angular velocity of a turntable as a function of time. What is its average angular acceleration between t = 2 s and t = 4 s?
A) −10 rad/s2
B) −5 rad/s2
C) 0 rad/s2
D) 5 rad/s2
E) 10 rad/s2
Difficulty: E
Section: 10.1
Learning Objective 10.1.11
32. A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is:
A) 63 rad/s
B) 75 rad/s
C) 89 rad/s
D) 130 rad/s
E) 210 rad/s
Difficulty: H
Section: 10-1
Learning Objective 10.1.12
33. A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of:
A) 1.7 s
B) 2.6 s
C) 3.0 s
D) 4.4 s
E) 9.0 s
Difficulty: E
Section: 10-1
Learning Objective 10.1.12
34. A wheel starts from rest and has an angular acceleration that is given by (t) = 6 rad/s4)t2. The angle through which it turns in time t is given by:
A) [(1/8)t4] rad/s4
B) [(1/4)t4] rad/s4
C) [(1/2)t4] rad/s4
D) (t4) rad/s4
E) 12 rad
Difficulty: E
Section: 10-1
Learning Objectives 10.1.12, 10.1.13
35. A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. The time it takes to make 10 rev is:
A) 1.3 s
B) 2.1 s
C) 2.8 s
D) 3.3 s
E) 4.0 s
Difficulty: M
Section: 10-1
Learning Objectives 10.1.12, 10.1.13
36. A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is:
A) 3.3 rad/s
B) 4.4 rad/s
C) 6.7 rad/s
D) 11 rad/s
E) 48 rad/s
Difficulty: M
Section: 10-2
Learning Objective 10.2.1
37. A wheel rotates with a constant angular acceleration of rad/s2. During a certain time interval its angular displacement is rad. At the end of the interval its angular velocity is 2 rad/s. Its angular velocity at the beginning of the interval is:
A) 0 rad/s
B) 1 rad/s
C) rad/s
D) rad/s
E) 2 rad/s
Difficulty: M
Section: 10-2
Learning Objective 10.2.1
38. A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through:
A) 81 rad
B) 160 rad
C) 245 rad
D) 330 rad
E) 410 rad
Difficulty: M
Section: 10-2
Learning Objective 10.2.1
39. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:
A) 8.9 rad/s
B) 16 rad/s
C) 22 rad/s
D) 32 rad/s
E) 250 rad/s
Difficulty: M
Section: 10-2
Learning Objective 10.2.1
40. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is:
A) 0.50 s
B) 0.71 s
C) 2.2 s
D) 2.8 s
E) 5.6 s
Difficulty: E
Section: 10-2
Learning Objective 10.2.1
41. A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s2. The cord will unwind in:
A) 0.82 s
B) 2.0 s
C) 12 s
D) 16 s
E) 130 s
Difficulty: M
Section: 10-2
Learning Objective 10.2.1
42. The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:
A) 7.0 m/s
B) 14 rad/s
C) 7 rad/s
D) 0.70 m/s
E) none of these
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
43. A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:
A) 0.10 m/s2
B) 0.50 m/s2
C) 500 m/s2
D) 2.5 m/s2
E) 102 m/s2
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
44. A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is:
A) vertically upward
B) horizontally to the north
C) horizontally to the south
D) zero
E) upward and forward at 45 to the horizontal
Difficulty: E
Section: 10-3
Learning Objective 10.3.0
45. Wrapping paper is being unwrapped from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:
A) 2.0 rad/s
B) 5.0 rad/s
C) 10 rad/s
D) 25 rad/s
E) 50 rad/s
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
46. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, the segment’s acceleration changes by:
A) 0 m/s2
B) 0.010 m/s2
C) 0.020 m/s2
D) 0.10 m/s2
E) 0.20 m/s2
Difficulty: M
Section: 10-3
Learning Objective 10.3.1
47. A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:
A) 5.0 rad/s2
B) 3.0 m/s2
C) 5.0 m/s2
D) 6.0 m/s2
E) 12 m/s2
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
48. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
A) 1
B) 2
C) 1/2
D) 4
E) 1/4
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
49. For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:
A) 1
B) 2
C) 1/2
D) 4
E) 1/4
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
50. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:
A) 1
B) 2
C) 1/2
D) 4
E) 1/4
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
51. Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:
A) 1
B) 2
C) 1/2
D) 4
E) 1/4
Difficulty: E
Section: 10-3
Learning Objective 10.3.1
52. The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
A) the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4
B) the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed
C) the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2
D) the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E) the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4
Difficulty: M
Section: 10-3
Learning Objectives 10.3.1, 10.3.2
53. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:
A) decreases in magnitude and becomes more nearly tangent to the rim
B) decreases in magnitude and becomes more nearly radial
C) increases in magnitude and becomes more nearly tangent to the rim
D) increases in magnitude and becomes more nearly radial
E) increases in magnitude but retains the same angle with the tangent to the rim
Difficulty: M
Section: 10-3
Learning Objective 10.3.1
54. Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.
A) 1, 2, 3
B) 3, 2, 1
C) 3, then 1 and 2 tie
D) 1, 3, 2
E) All are the same
Difficulty: E
Section: 10-4
Learning Objective 10.4.1
55. Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:
A) 4.0 kg∙m2
B) 12 kg∙m2
C) 9.6 kg∙m2
D) 4.8 kg∙m2
E) none of these
Difficulty: E
Section: 10-4
Learning Objective 10.4.2
56. Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:
A) ML2/2
B) ML2
C) 3ML2/2
D) 6ML2
E) 3ML2
Difficulty: E
Section: 10-4
Learning Objective 10.4.2
57. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 10–3 kg∙m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is:
A) 2.0 J
B) 12 J
C) 14 J
D) 22 J
E) 28 J
Difficulty: M
Section: 10-4
Learning Objective 10.4.3
58. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 10–3 kg∙m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is:
A) the heavier block
B) the lighter block
C) the pulley
D) either block (the two blocks have the same kinetic energy)
E) none (all three objects have the same kinetic energy)
Difficulty: M
Section: 10-4
Learning Objective 10.4.3
59. The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is:
A) MR2/2
B) ML2/2
C) ML2
D) MR2
E) none of these
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
60. The rotational inertia of a wheel about its axle does not depend upon its:
A) diameter
B) mass
C) distribution of mass
D) speed of rotation
E) material composition
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
61. Consider four objects, each having the same mass and the same radius:
1. a solid sphere
2. a hollow sphere
3. a flat disk in the x,y plane
4. a hoop in the x,y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:
A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 1, 3, 2, 4
D) 4, 2, 3, 1
E) 3, 1, 2, 4
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
62. A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X─X' is:
A) 2
B) 4
C) 8
D) 16
E) 32
Difficulty: M
Section: 10-5
Learning Objective 10.5.1
63. Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:
A) the one made from the more dense material
B) the one made from the less dense material
C) neither — both rotational inertias are the same
D) the disk with the larger angular velocity
E) the disk with the larger torque
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
64. A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is:
A) greater
B) less
C) same
D) unknown unless the radii are given
E) unknown unless both the masses and the radii are given
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
65. To increase the rotational inertia of a solid disk about its axis without changing its mass:
A) drill holes near the rim and put the material near the axis
B) drill holes near the axis and put the material near the rim
C) drill holes at points on a circle near the rim and put the material at points between the holes
D) drill holes at points on a circle near the axis and put the material at points between the holes
E) do none of the above (the rotational inertia cannot be changed without changing the mass)
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
66. The rotational inertia of a disk about its axis is 0.70 kgm2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:
A) 0.32 kgm2
B) 0.54 kgm2
C) 0.70 kgm2
D) 0.86 kgm2
E) 1.0 kgm2
Difficulty: E
Section: 10-5
Learning Objective 10.5.1
67. A thin rod of length L has a density that increases along its length, ρ = ρ0x. What is the rotational inertia of the rod around its less dense end?
A) ML2/12
B) ML2/6
C) ML2/3
D) ML2/2
E) ML2
Difficulty: H
Section: 10-5
Learning Objective 10.5.2
68. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:
A) ML2/12
B) ML2/6
C) ML2/3
D) 7ML2/12
E) 13ML2/12
Difficulty: E
Section: 10-5
Learning Objective 10.5.3
69. The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:
A) MR2
B) (2/5)MR2
C) (3/5)MR2
D) (5/2)MR2
E) (7/5)MR2
Difficulty: E
Section: 10-5
Learning Objective 10.5.3
70. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:
A) (2/5)MR2
B) 9MR2
C) 16MR2
D) 47/5MR2
E) (82/5)MR2
Difficulty: E
Section: 10-5
Learning Objective 10.5.3
71. The torque exerted on an object can be written as
. Here,
:
A) is the radius of the object.
B) is a vector pointing from the axis of rotation to the point where the force is applied.
C) is always perpendicular to
.
D) is a vector pointing from the point where the force is applied to the axis of rotation.
E) points along the axis of rotation.
Difficulty: E
Section: 10-6
Learning Objective 10.6.1
72. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
A) applying the force near the axle, radially outward from the axle
B) applying the force near the rim, radially outward from the axle
C) applying the force near the axle, parallel to a tangent to the wheel
D) applying the force at the rim, tangent to the rim
E) applying the force at the rim, at 45 to the tangent
Difficulty: E
Section: 10-6
Learning Objective 10.6.2
73. The meter stick shown below rotates about an axis through the point marked , 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.
A) , , , ,
B) and tie, then , ,
C) and tie, then , ,
D) , , , and tie, then
E) and tie, then , then and tie
Difficulty: E
Section: 10-6
Learning Objective 10.6.2
74. A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is:
A) applied tangentially halfway between the axis and the rim
B) applied tangentially at the rim
C) applied radially halfway between the axis and the rim
D) applied radially at the rim
E) applied at the rim but neither radially nor tangentially
Difficulty: E
Section: 10-6
Learning Objective 10.6.2
75. A force is applied to a billiard ball. In order to calculate the torque created by the force, you also need to know:
A) the mass of the ball
B) the rotational inertia of the ball
C) the kinetic energy of the ball
D) the angular speed of the ball
E) the location and orientation of the axis of rotation of the ball
Difficulty: E
Section: 10-6
Learning Objective 10.6.3
76. The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot Which force(s) create a positive torque around that axis?
A) only
B) and
C) only
D) , and
E) only
Difficulty: E
Section: 10-6
Learning Objective 10.6.4
77. A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the pivot is:
A) 0 Nm
B) 5.0 Nm
C) 8.7 Nm
D) 15 Nm
E) 26 Nm
Difficulty: M
Section: 10-6
Learning Objective 10.6.5
78. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:
A) for all orientations of
B) for all orientations of
C) for all orientations of
D) for some orientations of and for others
E) for some orientations of and for others
Difficulty: E
Section: 10-6
Learning Objective 10.6.5
79. = Ifor an object rotating about a fixed axis, where is the net torque acting on it, I is its rotational inertia, and is its angular acceleration. This expression:
A) is the definition of torque
B) is the definition of rotational inertia
C) is the definition of angular acceleration
D) follows directly from Newton's second law
E) depends on a principle of physics that is unrelated to Newton's second law
Difficulty: E
Section: 10-7
Learning Objective 10.7.0
80. A uniform disk, a thin hoop, and a uniform solid sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular velocities after a given time t, least to greatest.
A) disk, hoop, sphere
B) disk, sphere, hoop
C) hoop, sphere, disk
D) hoop, disk, sphere
E) sphere, disk, hoop
Difficulty: E
Section: 10-7
Learning Objective 10.7.1
81. A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg m2. A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:
A) 2.5 rad/s2
B) 5.0 rad/s2
C) 10 rad/s2
D) 15 rad/s2
E) 20 rad/s2
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
82. A disk with a rotational inertia of 2.0 kgm2 and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is:
A) 0.40 rad/s2
B) 0.60 rad/s2
C) 1.0 rad/s2
D) 2.5 rad/s2
E) 10 rad/s2
Difficulty: E
Section: 10-7
Learning Objective 10.7.1
83. A disk with a rotational inertia of 5.0 kgm2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied along the rotation axis. The angular acceleration of the disk is:
A) 0 rad/s2
B) 0.40 rad/s2
C) 0.60 rad/s2
D) 1.0 rad/s2
E) 2.5 rad/s2
Difficulty: E
Section: 10-7
Learning Objective 10.7.1
84. A disk with a rotational inertia of 5.0 kg m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:
A) 0.57 rad/s
B) 0.64 rad/s
C) 0.80 rad/s
D) 1.6 rad/s
E) 3.2 rad/s
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
85. A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:
A) 7.0 N∙m
B) 14 N∙m
C) 28 N∙m
D) 44 N∙m
E) none of these
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
86. A certain wheel has a rotational inertia of 12 kg∙m2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:
A) 0.015 N∙m
B) 0.18 N∙m
C) 0.57 N∙m
D) 2.1 N∙m
E) 13 N∙m
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
87. An 8.0-cm radius disk with a rotational inertia of 0.12 kg∙m2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-Nm torque to the disk. The acceleration of the mass is:
A) 0.50 m/s2
B) 3.9 m/s2
C) 6.0 m/s2
D) 12 m/s2
E) 20 m/s2
Difficulty: H
Section: 10-7
Learning Objective 10.7.1
88. A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg∙m2. When the block is released and the cord unwinds, the acceleration of the block is:
A) 0.15 g
B) 0.56 g
C) 0.84 g
D) 1.0 g
E) 1.3 g
Difficulty: H
Section: 10-7
Learning Objective 10.7.1
89. A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the mass with a force of:
A) 6.9 N
B) 9.8 N
C) 16 N
D) 26 N
E) 29 N
Difficulty: H
Section: 10-7
Learning Objective 10.7.1
90. A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The acceleration of the block is:
A) R1F/mR2
B) R1R2F/(I – mR22)
C) R1R2F/(I + mR22)
D) R1R2F/(I – mR1R2)
E) R1R2F/(I + mR1R2)
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
91. A small disk of radius R1 is fastened coaxially to a larger disk of radius R2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The tension in the string pulling the block is:
A) R1F/R2
B) mR1R2F/(I – mR22)
C) mR1R2F/(I + mR22)
D) mR1R2F/(I – mR1R2)
E) mR1R2F/(I + mR1R2)
Difficulty: M
Section: 10-7
Learning Objective 10.7.1
92. A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:
A) pulls on both blocks, but exerts a greater force on the heavier block
B) pulls on both blocks, but exerts a greater force on the lighter block
C) pulls on both blocks and exerts the same magnitude force on both blocks
D) does not pull on either block
E) pulls only on the lighter block
Difficulty: E
Section: 10-7
Learning Objective 10.7.1
93. A disk with a rotational inertia of 5.0 kg∙m2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:
A) 1.6 J
B) 2.5 J
C) 6.3 J
D) 10 J
E) 40 J
Difficulty: E
Section: 10-8
Learning Objective 10.8.1
94. A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N∙m on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:
A) 0 J
B) 480 J
C) 960 J
D) 1500 J
E) 1800 J
Difficulty: E
Section: 10-8
Learning Objective 10.8.1
95. A disk has a rotational inertia of 6.0 kg∙m2 and a constant angular acceleration of 2.0 rad/s2. If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:
A) 0 J
B) 30 J
C) 60 J
D) 300 J
E) 600 J
Difficulty: M
Section: 10-8
Learning Objective 10.8.1
96. A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.
A) the same
B) half as much
C) twice as much
D) three times as much
E) four times as much
Difficulty: M
Section: 10-8
Learning Objective 10.8.1
97. A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The work done by the torque during the second revolution is ______ as the work done during the first revolution.
A) the same
B) twice as much
C) half as much
D) four times as much
E) one fourth as much
Difficulty: M
Section: 10-8
Learning Objective 10.8.1
98. A torque of 170 N∙m does 4700 J of work on a rotating flywheel. If the flywheel’s initial kinetic energy is 1500 J, what is its final kinetic energy?
A) 1500 J
B) 3200 J
C) 4700 J
D) 6200 J
E) cannot be calculated without knowing the rotational inertia of the flywheel
Difficulty: E
Section: 10-8
Learning Objective 10.8.2
99. A constant torque of 260 N∙m acts on a flywheel. If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel?
A) 1.7 J
B) 41 J
C) 600 J
D) 6.5 x 103 J
E) 4.1 x 104 J
Difficulty: E
Section: 10-8
Learning Objective 10.8.3
100. A constant torque of 260 N∙m acts on a flywheel. If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque?
A) 54 W
B) 200 W
C) 340 W
D) 3.3 x 103 W
E) 2.0 x 104 W
Difficulty: E
Section: 10-8
Learning Objective 10.8.4
101. A torque of 470 N∙m acts on a flywheel. At the instant that the flywheel’s angular speed is 56 rad/s, at what rate is work being done by the torque?
A) 8.4 W
B) 26 W
C) 112 W
D) 4200 W
E) 2.6 x 104 W
Difficulty: E
Section: 10-8
Learning Objective 10.8.5