Deck 8: Torque and Angular Momentum

Question 1

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.

Answer 1

8.7 N.m.

Question 2

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.

Answer 2

14.1 N.m.

Question 3

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).If this system of masses rotated about the Y-axis perpendicular to the Z-X plane,then the moment of inertia of this system is

A) 73 kg m².
B) 66 kg m².
C) 60 kg m².
D) 55 kg m².
E) 48 kg m².

Answer 3

73 kg m².

Question 4

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) (10/7m,8/7m,11/7m).
B) (11/7m,7/7m,8/7m).
C) (7/7m,10/7m,11/7m).
D) (10/7m,7/7m,8/7m).
E) (8/7m,7/7m,10/7m).

Question 5

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L?

A) 0.123 ML²
B) 0.198 ML²
C) 0.205 ML²
D) 0.240 ML²
E) 0.300 ML²

Question 6

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.

Question 7

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

A) 0.080 ML²
B) 0.072 ML²
C) 0.068 ML²
D) 0.060 ML²
E) 0.056 ML²

Question 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).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A) 281 kg m².
B) 167 kg m².
C) 113 kg m².
D) 85 kg m².
E) 69 kg m².

Question 9

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).

Question 10

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.

Question 11

A centrifuge has a rotational inertia of 5.50 $\times$ 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

Question 12

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).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A) 23 kg m².
B) 28 kg m².
C) 33 kg m².
D) 36 kg m².
E) 41 kg m².

Question 13

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).If this system of masses rotated about the Y-axis perpendicular to the X-Z plane,then the moment of inertia of this system is

A) 40 kg m².
B) 32 kg m².
C) 29 kg m².
D) 24 kg m².
E) 19 kg m².

Question 14

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.

Question 15

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 through the center and perpendicular to it?

A) 0.980 kg m²
B) 0.761 kg m²
C) 1.85 kg m²
D) 2.29 kg m²

Question 16

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).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

A) 50 kg m².
B) 55 kg m².
C) 58 kg m².
D) 62 kg m².
E) 68 kg m².

Question 17

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).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A) 24 kg m².
B) 36 kg m².
C) 43 kg m².
D) 56 kg m².
E) 62 kg m².

Question 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).

Question 19

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.

Question 20

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).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

A) 60 kg m².
B) 79 kg m².
C) 85 kg m².
D) 98 kg m².
E) 112 kg m².

Question 21

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 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

Question 22

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 and 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

Question 23

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.

Question 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 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.

Question 25

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.

Question 26

A 75.0 kg ladder that is 3.00 m in length 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 makes 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

Question 27

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.

Question 28

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.

Question 29

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 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.

Question 30

A 2.00 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

Question 31

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 and 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

Question 32

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 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.

Question 33

A 75.0 kg ladder that is 3.00 m in length 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

Question 34

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

Question 35

A 75.0 kg ladder that is 3.00 m in length 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 makes 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

Question 36

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) (5/15m,-1/15m,17/15m).
B) (5/15m,-17/15m,5/15m).
C) (12/15m,-5/15m,16/15m).
D) (7/15m,-5/15m,16/15m).
E) (16/15m,-1/15m,17/15m).

Question 37

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 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.

Question 38

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.

Question 39

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) (1/10m,10/10m,1/10m).
B) (2/10m,0m,11/10m).
C) (3/10m,2/10m,10/10m).
D) (10/10m,2/10m,3/10m).
E) (2/10m,10/10m,0m).

Question 40

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

Question 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 cm and a moment of inertia of 1/2 MR².If m₁ is 4.00 kg,m₂ is 2.00 kg,and M is 4.00 kg,then what is the 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

Question 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 1/2 MR².If m₁ is 4.00 kg,m₂ is 4.00 kg,and M is 4.00 kg,then what is the 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

Question 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 1/2 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

Question 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 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
B) 2.89 m/s²
C) 2.43 m/s²
D) 2.15 m/s²
E) 1.49 m/s²

Question 45

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

Question 46

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

Question 47

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 1/2 MR².If m₁ is 3.00 kg,m₂ is 6.00 kg and M is 4.00 kg,then what is 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

Question 48

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 1/2 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

Question 49

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 1/2 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

Question 50

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 angular 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.

Question 51

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 angular 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.

Question 52

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 1/2 MR².If m₁ is 1.00 kg,m₂ is 2.00 kg,and M is 4.00 kg,then what is the 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

Question 53

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 1/2 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

Question 54

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.

Question 55

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.

Question 56

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 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

Question 57

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 1/2 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

Question 58

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 1/2 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

Question 59

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 1/2 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

Question 60

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 1/2 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

Question 61

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) 1.75 m/s.

Question 62

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.

Question 63

A pole-vaulter holds out a 5.5kg,4.75m 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 0.75m from the end,what is the torque applied by the Earth to the pole?

A) 40N
B) 88N
C) Not enough information is given
D) 128N

Question 64

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

Question 65

A 1.5m long,0.75kg 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 1.5kg.(The center of the brass weight is 1.5m 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 Nm
B) 28 Nm
C) 9.5 Nm
D) 25 Nm

Question 66

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) 1.72 m/s.
E) 1.98 m/s.

Question 67

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 1.5kg.(The center of the brass weight is 1.5m 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) 8.4Nm
B) 22 Nm
C) 20 Nm
D) 9.1 Nm

Question 68

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

Question 69

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

Question 70

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.

Question 71

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.

Question 72

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/s,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

Question 73

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.

Question 74

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.

Question 75

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

A) 5500 Nm
B) 7500Nm
C) 0 Nm
D) 2000 Nm
E) Cannot determine

Question 76

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/s,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

Question 77

A piston in an internal combustion engine applies torque during 150^o 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 2500rpm and produces 410J of work each second.What is the torque applied to the crank shaft by one of the engine's eight pistons?

A) 3.8 Nm
B) 1.6 Nm
C) 0.47Nm
D) 0.20 Nm

Question 78

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.

Question 79

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

A) 190 J
B) 150 J
C) 290 J
D) 130 J

Question 80

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.