Question 1

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?

Accepted Answer

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

Question 2

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

Accepted Answer

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 3

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

Accepted Answer

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 4

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

Accepted Answer

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.

Question 5

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?

Accepted Answer

A)  35 degrees 
B)  45 degrees 
C)  53 degrees 
D)  60 degrees 
E)  65 degrees

Question 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 (-1.0 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

Accepted Answer

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

Question 7

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

Accepted Answer

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 8

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

Accepted Answer

A)  0.19s 
B)  0.55s 
C)  2.4s 
D)  12s

Question 9

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?

Accepted Answer

A)  35.6 N 
B)  32.7 N 
C)  31.0 N 
D)  29.0 N 
E)  23.5 N

Question 10

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?

Accepted Answer

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 11

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?

Accepted Answer

A)  0.957 J 
B)  0.902 J 
C)  0.870 J 
D)  0.750 J 
E)  0.690 J

Question 12

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

Accepted Answer

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

Question 13

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?

Accepted Answer

A)  33.6 N 
B)  42.8 N 
C)  53.6 N 
D)  63.4 N 
E)  75.5 N

Question 14

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?

Accepted Answer

A)  625 N 
B)  640 N 
C)  735 N 
D)  832 N 
E)  900 N

Question 15

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

Accepted Answer

A)  3.02 J. 
B)  3.52 J. 
C)  3.75 J. 
D)  4.02 J. 
E)  4.23 J.

Question 16

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

Accepted Answer

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 17

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?

Accepted Answer

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

Question 18

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

Accepted Answer

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 19

A system in equilibrium cannot have

Accepted Answer

A)  any forces on it 
B)  a non-zero velocity 
C)  any torques on it 
D)  a non-zero acceleration

Question 20

A pole-vaulter holds out a 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 ratio of the force applied by the hand on the end of the pole to the weight of the pole?

Accepted Answer

A)  3.2 
B)  2.7 
C)  5.3 
D)  2.2

Exam 8: Torque and Angular Momentum

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 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 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 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 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 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

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 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 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 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

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 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 system in equilibrium cannot have

Exam 8: Torque and Angular Momentum

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 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 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 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 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 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

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 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 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 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

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 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 system in equilibrium cannot have

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 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 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

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 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