Ch8 Torque And Angular Momentum Exam Questions

Physics, 9e (Giambattista)

Chapter 8 Torque and Angular Momentum

1) A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the Z-axis, perpendicular to the X-Y plane, is

A) 50 kg m2.

B) 55 kg m2.

C) 58 kg m2.

D) 62 kg m2.

E) 68 kg m2.

2) A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

A) 23 kg m2.

B) 28 kg m2.

C) 33 kg m2.

D) 36 kg m2.

E) 41 kg m2.

3) What is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm, about an axis perpendicular to the disk and passing through its center?

A) 0.980 kg m2

B) 0.761 kg m2

C) 1.85 kg m2

D) 2.29 kg m2

4) A centrifuge has a rotational inertia of 5.50 × 10−3 kg m2. How much energy must be supplied to bring it from rest to 500 rad/s?

A) 627 J

B) 570 J

C) 688 J

D) 743 J

E) 583 J

5) A 4.00 kg mass is located at (2.00 m, 2.00 m, 0.00 m) and a 3.00 kg mass is located at (−1.0 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

A) 24 kg m2.

B) 36 kg m2.

C) 43 kg m2.

D) 56 kg m2.

E) 62 kg m2.

6) A 4.00 kg mass is located at (2.00 m, 2.00 m, 0.00 m) and a 3.00 kg mass is located at (−1 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the Y-axis, perpendicular to the X-Z plane, is

A) 40 kg m2.

B) 32 kg m2.

C) 29 kg m2.

D) 24 kg m2.

E) 19 kg m2.

7) A 6.00 kg mass is located at (2.00 m, 2.00 m, 2.00 m) and a 5.00 kg mass is located at (−1.0 m, 3.00 m, −2.00 m). The rotational inertia of this system of masses about the Z-axis, perpendicular to the X-Y plane, is

A) 60 kg m2.

B) 79 kg m2.

C) 85 kg m2.

D) 98 kg m2.

E) 112 kg m2.

8) A 6.00 kg mass is located at (2.00 m, 2.00 m, 2.00 m) and a 5.00 kg mass is located at (−1.0 m, 3.00 m, −2.00 m). The rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

A) 281 kg m2.

B) 167 kg m2.

C) 113 kg m2.

D) 85 kg m2.

E) 69 kg m2.

9) A 6.00 kg mass is located at (2.00 m, 2.00 m, 2.00 m) and a 5.00 kg mass is located at (−1.0 m, 3.00 m, −2.00 m). The rotational inertia of this system of masses about the Y-axis, perpendicular to the Z-X plane, is

A) 73 kg m2.

B) 66 kg m2.

C) 60 kg m2.

D) 55 kg m2.

E) 48 kg m2.

10) The rotational inertia of a thin rod about one end is 1/3 ML2. What is the rotational inertia of the same rod about a point located 0.300 L from the end?

A) 0.123 ML2

B) 0.198 ML2

C) 0.205 ML2

D) 0.240 ML2

E) 0.300 ML2

11) The rotational inertia of a thin rod about one end is 1/3 ML2. What is the rotational inertia of the same rod about a point located 0.40 L from the end?

A) 0.493 ML2

B) 0.243 ML2

C) 0.093 ML2

D) 0.073 ML2

E) 0.056 ML2

12) A 20.0 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied perpendicularly at the end of the wrench. The torque generated at the bolt is

A) 8.0 N·m.

B) 10 N·m.

C) 14 N·m.

D) 22 N·m.

E) 37 N·m.

13) A 30.0 cm wrench is used to generate a torque at a bolt. A force of 40 N is applied perpendicularly at the end of the wrench. The torque generated at the bolt is

A) 5.0 N·m.

B) 7.0 N·m.

C) 9.0 N·m.

D) 12 N·m.

E) 20 N·m.

14) A 20.0 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench. The torque generated at the bolt is

A) 4.9 N·m.

B) 5.7 N·m.

C) 6.0 N·m.

D) 7.5 N·m.

E) 8.7 N·m.

15) A 30.0 cm wrench is used to generate a torque at a bolt. A force of 50.0 N is applied at the end of the wrench at an angle of 70.0 degrees. The torque generated at the bolt is

A) 10.4 N·m.

B) 14.1 N·m.

C) 19.7 N·m.

D) 21.5 N·m.

E) 26.2 N·m.

16) A torque of 20.0 N·m is applied to a bolt. The bolt rotates through an angle of 180 degrees. The work done in turning the bolt is

A) 72.5 J.

B) 51.9 J.

C) 62.8 J.

D) 49.9 J.

E) 58.4 J.

17) A torque of 15.0 N.m is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

A) 94.2 J.

B) 91.3 J.

C) 96.7 J.

D) 89.9 J.

E) 98.1 J.

18) A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The center of gravity of the system of masses is

A) (1.33 m, 2.00 m, 0).

B) (1.33 m, 1.00 m, 0).

C) (1.50 m, 1.33 m, 0).

D) (2.00 m, 1.33 m, 0).

E) (1.33 m, 1.50 m, 0).

19) A 5.00 kg mass is located at (2.00 m, 0.00 m, 0.00 m) and a 3.00 kg mass is located at (0.00 m, 4.00 m, 0.00 m). The center of gravity of the system of masses is

A) (1.25 m, 1.25 m, 0).

B) (1.50 m, 1.50 m, 0).

C) (1.25 m, 1.50 m, 0).

D) (1.50 m, 1.25 m, 0).

E) (1.00 m, 1.00 m, 0).

20) A 5.00 kg mass is located at (2.00 m, 0.00 m, 3.00 m) and a 2.00 kg mass is located at (0.00 m, 4.00 m, –2.00 m). The center of gravity of the system of masses is

A) (10/7 m, 8/7 m, 11/7 m).

B) (11/7 m, 7/7 m, 8/7 m).

C) (7/7 m, 10/7 m, 11/7 m).

D) (10/7 m, 7/7 m, 8/7 m).

E) (8/7 m, 7/7 m, 10/7 m).

21) A 5.00 kg mass is located at (1.0 m, 0.00 m, 3.00 m), a 2.00 kg mass is located at (0.00 m, 3.00 m, −2.00 m), and a 3.00 kg mass is located at (−1.0 m , −2.00 m , 0.00 m). The center of gravity of the system of masses is

A) (1/10 m, 10/10 m, 1/10 m).

B) (2/10 m, 0 m, 11/10 m).

C) (3/10 m, 2/10 m, 10/10 m).

D) (10/10 m, 2/10 m, 3/10 m).

E) (2/10 m, 10/10 m, 0 m).

22) A 6.00 kg mass is located at (1.0 m, −2.00 m, 3.00 m), a 5.00 kg mass is located at (1.0 m, 3.00 m, −2.00 m), and a 4.00 kg mass is located at (−1.0 m, −2.00 m, 2.00 m). The center of gravity of the system of masses is

A) (5/15 m, −1/15 m, 17/15 m).

B) (5/15 m, −17/15 m, 5/15 m).

C) (12/15 m, −5/15 m, 16/15 m).

D) (7/15 m, −5/15 m, 16/15 m).

E) (16/15 m, −1/15 m, 17/15 m).

23) Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 100 N. Wayne weighs 800 N. Wayne's center of gravity is 75.0 cm from Chris. Chris and Jamie are at the ends of the stretcher. The upward force that Chris is exerting to support the stretcher, with Wayne on it, is

A) 250 N.

B) 350 N.

C) 400 N.

D) 550 N.

E) 650 N.

24) Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 100 N. Wayne weighs 800 N. Wayne's center of gravity is 75.0 cm from Chris. Chris and Jamie are at the ends of the stretcher. The upward force that Jamie is exerting to support the stretcher, with Wayne on it, is

A) 250 N.

B) 300 N.

C) 350 N.

D) 400 N.

E) 550 N.

25) Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 80 N. Bob weighs 600 N. Bob's center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The upward force that Mary is exerting to support the stretcher, with Bob on it, is

A) 550 N.

B) 400 N.

C) 300 N.

D) 280 N.

E) 200 N.

26) Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 80 N. Bob weighs 600 N. Bob's center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The upward force that Jim is exerting to support the stretcher, with Bob on it, is

A) 280 N.

B) 320 N.

C) 380 N.

D) 400 N.

E) 520 N.

27) A 2.00 m long horizontal uniform beam of mass 20.0 kg is supported by a wire as shown in the figure. The wire makes an angle of 20.0 degrees with the beam. Attached to the beam 1.40 m from the wall is a ball with a mass of 40.0 kg. What is the tension in the string?

A) 1,000 N

B) 1,090 N

C) 2,100 N

D) 2,250 N

E) 2,680 N

28) A 2.000 m long horizontal uniform beam of mass 20.00 kg is supported by a wire as shown in the figure. The wire makes an angle of 20.00 degrees with the beam. Attached to the beam 1.400 m from the wall is a ball with a mass of 40.00 kg. What are the vertical and horizontal components of the force of the wall on the beam at the hinge?

A) V = 175.6 N, H = 2,023 N

B) V = 186.6 N, H = 1,805 N

C) V = 195.4 N, H = 1,750 N

D) V = 200.6 N, H = 1,323 N

E) V = 215.6 N, H = 1,023 N

29) A 1.500 m long uniform beam of mass 30.00 kg is supported by a wire as shown in the figure. The beam makes an angle of 10.00 degrees with the horizontal and the wire makes an angle of 30.00 degrees with the beam. A 50.00 kg mass, m, is attached to the end of the beam. What is the tension in the wire?

A) 2,034 N

B) 1,855 N

C) 1,435 N

D) 1,255 N

E) 1,035 N

30) A 1.500 m long uniform beam of mass 30.00 kg is supported by a wire as shown in the figure. The beam makes an angle of 10.00 degrees with the horizontal and the wire makes an angle of 30.00 degrees with the beam. A 50.00 kg mass, m, is attached to the end of the beam. What are the vertical and horizontal components of the force of the wall on the beam at the hinge?

A) H = 1,458 N, V = 454.0 N

B) H = 1,300 N, V = 403.4 N

C) H = 1,179 N, V = 354.9 N

D) H = 979 N, V = 324.5 N

E) H = 750 N, V = 297.3 N

31) A 75.0 kg ladder that is 3.00 m long is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.20 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.800. There is no friction between the wall and the ladder. What is the vertical force of the ground on the ladder?

A) 625 N

B) 640 N

C) 735 N

D) 832 N

E) 900 N

32) A 75.0 kg ladder that is 3.00 m long is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.20 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.800. There is no friction between the wall and the ladder. What is the minimum angle the ladder must make with the horizontal for the ladder not to slip and fall?

A) 26.57 degrees

B) 30.34 degrees

C) 36.35 degrees

D) 40.55 degrees

E) 46.52 degrees

33) A 75.0 kg ladder that is 3.00 m long is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.2 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.400. There is no friction between the wall and the ladder. What is the minimum angle the ladder must make with the horizontal for the ladder not to slip and fall?

A) 35 degrees

B) 45 degrees

C) 53 degrees

D) 60 degrees

E) 65 degrees

34) A 10 kg object has a moment of inertia of 1.25 kg m2. If a torque of 2.5 N•m is applied to the object, the angular acceleration is

A) 10 rad/s2.

B) 8.0 rad/s2.

C) 6.0 rad/s2.

D) 4.0 rad/s2.

E) 2.0 rad/s2.

35) An 8.0 kg object has a moment of inertia of 1.00 kg m2. What torque is needed to give the object an angular acceleration of 1.5 rad/s2?

A) 3.0 N·m

B) 2.5 N·m

C) 2.0 N·m

D) 1.5 N·m

E) 1.0 N·m

36) A 10 kg sphere with a 25.0 cm radius has a moment of inertia of 2/5 MR2. If a torque of 2.0 N•m is applied to the object, the angular acceleration is

A) 1.0 rad/s2.

B) 2.0 rad/s2.

C) 4.0 rad/s2.

D) 6.0 rad/s2.

E) 8.0 rad/s2.

37) An 8.00 kg object has a moment of inertia of 1.50 kg m2. If a torque of 2.00 N•m is applied to the object, the angular acceleration is

A) 0.750 rad/s2.

B) 1.00 rad/s2.

C) 1.33 rad/s2.

D) 2.01 rad/s2.

E) 2.67 rad/s2.

38) A 5.00 kg object has a moment of inertia of 1.20 kg m2. What torque is needed to give the object an angular acceleration of 2.0 rad/s2?

A) 2.4 N·m

B) 2.6 N·m

C) 2.8 N·m

D) 3.0 N·m

E) 3.2 N·m

39) A 10 kg solid cylinder with a 50.0 cm radius has a moment of inertia of 1/2 MR2. If a torque of 2.0 N•m is applied to the object, the angular acceleration is

A) 1.0 rad/s2.

B) 1.6 rad/s2.

C) 1.8 rad/s2.

D) 2.1 rad/s2.

E) 2.3 rad/s2.

40) A torque of 2.00 N•m is applied to a 10.0 kg object to give it an angular acceleration. If the angular acceleration is 1.75 rad/s2, then the moment of inertia is

A) 1.95 kg m2.

B) 1.05 kg m2.

C) 1.14 kg m2.

D) 1.20 kg m2.

E) 1.35 kg m2.

41) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the downward acceleration of m1?

A) 1.55 m/s2

B) 1.96 m/s2

C) 2.06 m/s2

D) 2.33 m/s2

E) 2.72 m/s2

42) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m1?

A) 6.83 N

B) 7.03 N

C) 7.84 N

D) 8.02 N

E) 8.33 N

43) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m2?

A) 3.92 m/s2

B) 3.65 m/s2

C) 3.23 m/s2

D) 3.02 m/s2

E) 2.98 m/s2

44) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR2. If m1 is 4.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the downward acceleration of m1?

A) 4.9 m/s2

B) 4.5 m/s2

C) 4.1 m/s2

D) 3.9 m/s2

E) 3.7 m/s2

45) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 4.00 kg, m2 is 4.00 kg, and M is 4.00 kg, then what is the downward acceleration of m1?

A) 4.42 m/s2

B) 3.92 m/s2

C) 3.42 m/s2

D) 3.04 m/s2

E) 2.96 m/s2

46) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 4.00 kg, m2 is 4.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m1?

A) 35.6 N

B) 32.7 N

C) 31.0 N

D) 29.0 N

E) 23.5 N

47) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 4.00 kg, m2 is 4.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m2?

A) 10.4 N

B) 12.6 N

C) 15.7 N

D) 17.6 N

E) 19.8 N

48) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30.0 cm and a moment of inertia of MR2. If m1 is 4.00 kg, m2 is 3.00 kg and M is 6.00 kg, then what is the magnitude of the acceleration of the masses?

A) 0.695 m/s2

B) 0.703 m/s2

C) 0.731 m/s2

D) 0.754 m/s2

E) 0.805 m/s2

49) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30.0 cm and a moment of inertia of MR2. If m1 is 4.00 kg, m2 is 3.00 kg and M is 6.00 kg, then what is the tension in the string that is attached to m1?

A) 36.2 N

B) 44.6 N

C) 58.2 N

D) 60.6 N

E) 74.5 N

50) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30.0 cm and a moment of inertia of MR2. If m1 is 4.00 kg, m2 is 3.00 kg and M is 6.00 kg, then what is the tension in the string that is attached to m2?

A) 20.7 N

B) 25.5 N

C) 31.7 N

D) 35.2 N

E) 41.3 N

51) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20.0 cm and a moment of inertia of ½ MR2. If m1 is 3.00 kg, m2 is 6.00 kg and M is 4.00 kg, then what is the magnitude of the acceleration of the masses?

A) 5.05 m/s2

B) 4.75 m/s2

C) 4.05 m/s2

D) 3.44 m/s2

E) 2.67 m/s2

52) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20.0 cm and a moment of inertia of ½ MR2. If m1 is 3.00 kg, m2 is 6.00 kg and M is 4.00 kg, then what is the tension in the string that is attached to mass m1?

A) 20.8 N

B) 27.4 N

C) 30.2 N

D) 37.4 N

E) 43.5 N

53) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20.0 cm and a moment of inertia of ½ MR2. If m1 is 3.00 kg, m2 is 6.00 kg and M is 4.00 kg, then what is the tension in the string that is attached to mass m2?

A) 33.6 N

B) 42.8 N

C) 53.6 N

D) 63.4 N

E) 75.5 N

54) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 2.00 kg, m2 is 1.00 kg, M is 4.00 kg, and the angle is 60.0 degrees, then what is the acceleration of m1?

A) 3.98 m/s2 down

B) 3.27 m/s2 down

C) 3.15 m/s2 down

D) 2.94 m/s2 down

E) 1.64 m/s2 down

55) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, M is 4.00 kg, and the angle is 60.0 degrees, then what is the acceleration of m1?

A) 0.00 m/s2

B) 1.20 m/s2

C) 1.80 m/s2

D) 2.20 m/s2

E) 2.80 m/s2

56) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 30.0 cm and a moment of inertia of MR2. If m1 is 4.00 kg, m2 is 4.00 kg, M is 4.00 kg, and the angle is 70.0 degrees, then what is the acceleration of m1?

A) 3.10 m/s2 down

B) 2.89 m/s2 down

C) 2.43 m/s2 down

D) 2.15 m/s2 down

E) 1.49 m/s2 down

57) A 4.00 kg solid sphere (I = 2/5 MR2) is spinning with an angular velocity of 23.0 rad/s. The diameter of the sphere is 20.0 cm. The rotational kinetic energy of the spinning sphere is

A) 3.02 J.

B) 3.52 J.

C) 3.75 J.

D) 4.02 J.

E) 4.23 J.

58) A 20.0 kg hollow cylinder (I = MR2) has a diameter of 50.0 cm. The cylinder is rolling down a hill with a velocity of 5.00 m/s. The rotational kinetic energy of the rolling cylinder is

A) 225 J.

B) 200 J.

C) 175 J.

D) 150 J.

E) 250 J.

59) A 4.00 kg hollow sphere (I = 2/3 MR2) is spinning with an angular velocity of 10.0 rad/s. The diameter of the sphere is 20.0 cm. The rotational kinetic energy of the spinning sphere is

A) 1.75 J.

B) 1.50 J.

C) 1.33 J.

D) 0.90 J.

E) 0.75 J.

60) A 4.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the hollow sphere is

A) 2.00 m/s2.

B) 2.22 m/s2.

C) 2.50 m/s2.

D) 2.64 m/s2.

E) 2.94 m/s2.

61) A 4.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

A) 1.28 m/s.

B) 1.44 m/s.

C) 1.65 m/s.

D) 1.71 m/s.

E) 1.98 m/s.

62) A 2.00 kg hollow sphere of radius 6.00 cm starts from rest and rolls without slipping down a 10.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

A) 1.51 m/s.

B) 1.47 m/s.

C) 1.22 m/s.

D) 1.01 m/s.

E) 1.95 m/s.

63) A 3.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 15.0 degree incline. If the length of the incline is 100 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

A) 3.02 m/s.

B) 2.59 m/s.

C) 2.37 m/s.

D) 2.02 m/s.

E) 1.74 m/s.

64) A 4.00 kg hollow cylinder of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the cylinder is

A) 2.45 m/s2.

B) 2.98 m/s2.

C) 3.35 m/s2.

D) 3.98 m/s2.

E) 4.05 m/s2.

65) A 4.00 kg hollow cylinder of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the cylinder at the bottom of the incline is

A) 1.35 m/s.

B) 1.82 m/s.

C) 1.57 m/s.

D) 2.55 m/s.

E) 3.02 m/s.

66) A 4.00 kg solid sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the solid sphere is

A) 1.50 m/s2.

B) 2.00 m/s2.

C) 2.50 m/s2.

D) 3.00 m/s2.

E) 3.50 m/s2.

67) A 4.00 kg solid sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the solid sphere at the bottom of the incline is

A) 1.69 m/s.

B) 1.87 m/s.

C) 2.33 m/s.

D) 2.75 m/s.

E) 3.22 m/s.

68) A 100 kg solid spherical rock (I = 2/5 MR2) has a diameter of 50.0 cm. The rock is rolling down a hill with a velocity of 5.00 m/s. The total kinetic energy (angular + translational) of the rolling rock is

A) 1,750 J.

B) 2,000 J.

C) 2,250 J.

D) 2,670 J.

E) 2,900 J.

69) A 2.00 kg solid sphere (I = 2/5 MR2) with a diameter of 50.0 cm is rotating at an angular velocity of 5.0 rad/s. The angular momentum of the rotating sphere is

A) 0.55 kg m2/s.

B) 0.48 kg m2/s.

C) 0.37 kg m2/s.

D) 0.25 kg m2/s.

E) 0.20 kg m2/s.

70) An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.00 rad/s. Her moment of inertia with her arms stretched out is 2.48 kg m2. What is her angular velocity when she pulls in her arms to make her moment of inertia 1.40 kg m2?

A) 2.67 rad/s

B) 2.45 rad/s

C) 2.03 rad/s

D) 1.90 rad/s

E) 1.77 rad/s

71) An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.00 rad/s. Her moment of inertia with her arms stretched out is 2.48 kg m2. What is the increase in her rotational kinetic energy when she pulls in her arms to make her moment of inertia 1.40 kg m2?

A) 0.957 J

B) 0.902 J

C) 0.870 J

D) 0.750 J

E) 0.690 J

72) A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m2. A torque of 100 N•m is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds?

A) 650 kg m2/s

B) 500 kg m2/s

C) 450 kg m2/s

D) 300 kg m2/s

E) 250 kg m2/s

73) A 10 kg solid cylinder (I = 1/2 MR2) with a radius of 30.0 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25 kg m2/s2, then what is the torque?

A) 70 N·m

B) 45 N·m

C) 37 N·m

D) 25 N·m

E) 12 N·m

74) A 10 kg solid cylinder (I = 1/2 MR2) with a radius of 30.0 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25.0 kg m2/s2, then what is the angular acceleration?

A) 75.3 rad/s2

B) 65.9 rad/s2

C) 55.6 rad/s2

D) 40.5 rad/s2

E) 35.2 rad/s2

75) A pirate demands that his 75 kg prisoner "walk the plank". The prisoner walks out on an 8.0 m long, 50 kg horizontal board that juts out from the side of the pirate ship. If he walks out and stands 7.5 m from the place where the board is connected to the ship's side, what is the net torque applied to the board?

A) 5500 N·m

B) 7500 N·m

C) 0 N·m

D) 2000 N·m

E) Cannot determine

76) A pole-vaulter holds out a 5.5 kg, 4.75 m long pole horizontally in front of him.  Assuming the pole is uniform in construction, and that he holds the pole with one hand at the very end, and one hand 0.75 m from the end, what is the torque applied by the gravitational force to the pole?

A) 40 N

B) 88 N

C) Not enough information is given

D) 128 N

77) A 1.5m long dowel (a cylindrical rod) is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane. The dowel has a diameter of 2.0 cm, and its density is 3.2 g/cm3. When it is positioned in its swing such that its angle with the vertical is 22.5 degrees, what is the torque on the rod about the pivot due to its weight?

A) 1.7 N·m

B) 4.2 N·m

C) 1.1 N·m

D) 1.0 N·m

E) 4.4 N·m

F) 4.1 N·m

78) A 1.5m long dowel is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane.  At the other end of the dowel is a brass weight having mass 1.5 kg.  (The center of the brass weight is 1.5 m from the pivot point. When the rod is positioned in its swing such that its angle with the vertical is 22.5 degrees, what is the torque on the rod about the pivot due to the presence of the brass weight?

A) 8.4 N·m

B) 22 N·m

C) 20 N·m

D) 9.1 N·m

79) A 1.5 m long, 0.75 kg dowel is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane. At the other end of the dowel is a brass weight having mass 1.5 kg. (The center of the brass weight is 1.5 m from the pivot point.)  When the rod is positioned in its swing such that its angle with the vertical is 22.5 degrees, what is the net torque on the rod about the pivot?

A) 11 N·m

B) 28 N·m

C) 10.5 N·m

D) 25 N·m

80) A piston in an internal combustion engine applies torque during 150° of each full rotation of the crankshaft to which it is connected.  Suppose an 8-cylinder engine (8 such pistons) is running with its crankshaft turning at 2500 rpm and produces 410 J of work each second.  What is the average torque applied to the crank shaft by one of the engine's eight pistons?

A) 3.8 N·m

B) 1.6 N·m

C) 0.47 N·m

D) 0.20 N·m

81) A fire fighter tightens the nut on the top of a fire hydrant using a large wrench.  If she applies a force of 250 N perpendicular to the wrench, at a point 0.75 m from the axis of rotation of the nut, how much work does she do on the nut as she rotates it through 45°?

A) 190 J

B) 150 J

C) 290 J

D) 130 J

82) A propeller is spun up from rest to 1500 rpm in 15.0 s under the influence of a constant torque.  If the work done by the engine in giving the propeller its final angular velocity is 25 kJ, what is the torque supplied by the engine?

A) 21 N·m

B) 11 N·m

C) 42 N·m

D) 3.4 N·m

E) 130 N·m

83) A 55 kg girl swings on a swing, whose seat is attached to the pivot by 2.5 m long rigid rods (considered to be massless in this problem).  As she swings, she rises to a maximum height such that the angle of the rods with respect to the vertical is 32 degrees.   What is the maximum torque on the rods due to her weight, as she moves during one cycle of her swinging from the bottom of her swing path to the highest point? 

A) 710 N·m

B) 970 N·m

C) 2400 N·m

D) 2000 N·m

84) A brake pad is used to give a normal force of 150 N to the outer surface of a 0.25 kg spinning disk, in order to slow it down from 250 rpm to rest.  The disk's radius is 0.25 m.  If the coefficient of friction between the pad and the disk is 0.45, how much time is required for the disk to slow from 250 rpm to rest?

A) 0.19 ms

B) 0.55 ms

C) 2.4 ms

D) 12 ms

85) A pole-vaulter holds out a 4.75 m pole horizontally in front of him.  Assuming the pole is uniform in construction, and that he holds the pole with one hand at the very end, and one hand 0.75 m from the end, what is the ratio of the force applied by the hand on the end of the pole to the weight of the pole?

A) 3.2

B) 2.7

C) 5.3

D) 2.2

86) An auto mechanic is attempting to loosen a bolt in an engine using a large wrench, but to no avail.  If she applies a force of 510 N perpendicular to the wrench she is using, applied at 0.75 m from the axis of rotation of the bolt, what is the value of the friction force applied to the outer surface of the bolt's threads?  The threaded portion of the bolt has diameter 1.2 cm. 

A) 3.2 kN

B) 16 N

C) 32 kN

D) 1.6 kN

E) 64 kN

87) A 0.50 kg solid disk spins at 250 rpm. A torque of 12.5 N·m is applied for 0.150 s to bring it to rest. What is the disk's radius?

A) 0.54 m

B) 0.38 m

C) 0.29 m

D) 0.14 m

88) An irregularly shaped object is attached to an axle so that it may be spun. If a torque of 250 N·m must be applied for 1.25 s in order to give it a rotation period of 0.10 s, what is its moment of inertia?

A) 5.0 kg m2

B) 31 kg m2

C) 4.0 kg m2

D) 25 kg m2

89) A 25.0 kg propeller may be considered to be a 4.5 m long, thin rod, spun about its center. Assuming the propeller starts from rest, What angular velocity will it have if a torque of 1100 N·m is applied for 1.2 s?

A) 31 rad/s

B) 26 rad/s

C) 7.8 rad/s

D) 2.6 rad/s

90) A system in equilibrium cannot have

A) any forces on it.

B) a non-zero velocity.

C) any torques on it.

D) a non-zero acceleration.

91) Which of the following objects has the greatest rotational kinetic energy? Each has mass M and radius R, and rotates with angular velocity ω.

A) a solid sphere

B) a solid cylinder

C) a thin-walled spherical shell

D) a thin-walled cylindrical shell

E) all have the same rotational KE

92) A thin rod is pivoted around its end, and an identical rod around its center. If they are to have the same rotational kinetic energy, then ωend/ωcenter =

A) 2

B) 1

C) 1/2

D) 1/4

E) 4

93) A person rides a bicycle along a straight road. From the point of view of the rider, what's the direction of the angular momentum vector of the front wheel?

A) up

B) down

C) left

D) right

E) forward

F) backward