Question 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 center of gravity of the system of masses is

Accepted Answer

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). 
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 2

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

Accepted Answer

A)  280 N. 
B)  320 N. 
C)  380 N. 
D)  400 N. 
E)  520 N. 
A)  280 N. 
B)  320 N. 
C)  380 N. 
D)  400 N. 
E)  520 N.

Question 3

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?

Accepted Answer

A)  2,034 N 
B)  1,855 N 
C)  1,435 N 
D)  1,255 N 
E)  1,035 N 
A)  2,034 N 
B)  1,855 N 
C)  1,435 N 
D)  1,255 N 
E)  1,035 N

Question 4

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

Accepted Answer

A)  225 J. 
B)  200 J. 
C)  175 J. 
D)  150 J. 
E)  250 J. 
A)  225 J. 
B)  200 J. 
C)  175 J. 
D)  150 J. 
E)  250 J.

Question 5

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

Accepted Answer

A)  94.2 J. 
B)  91.3 J. 
C)  96.7 J. 
D)  89.9 J. 
E)  98.1 J. 
A)  94.2 J. 
B)  91.3 J. 
C)  96.7 J. 
D)  89.9 J. 
E)  98.1 J.

Question 6

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?

Accepted Answer

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 
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 7

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?

Accepted Answer

A)  70 N.m 
B)  45 N.m 
C)  37 N.m 
D)  25 N.m 
E)  12 N.m 
A)  70 N.m 
B)  45 N.m 
C)  37 N.m 
D)  25 N.m 
E)  12 N.m

Question 8

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?

Accepted Answer

A)  10.4 N 
B)  12.6 N 
C)  15.7 N 
D)  17.6 N 
E)  19.8 N 
A)  10.4 N 
B)  12.6 N 
C)  15.7 N 
D)  17.6 N 
E)  19.8 N

Question 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).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

Accepted Answer

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

Question 10

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

Accepted Answer

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. 
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 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 her angular velocity when she pulls in her arms to make her moment of inertia 1.40 kg m2?

Accepted Answer

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 
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 12

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?

Accepted Answer

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

Question 13

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

Accepted Answer

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). 
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 14

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?

Accepted Answer

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

Question 15

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

Accepted Answer

A)  10 rad/s2. 
B)  8.0 rad/s2. 
C)  6.0 rad/s2. 
D)  4.0 rad/s2. 
E)  2.0 rad/s2. 
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 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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. 
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.

Question 19

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$^{\circ}$?

Accepted Answer

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

Question 20

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

Accepted Answer

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. 
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.

Exam 8: Torque and Angular Momentum

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

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 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 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 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 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 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 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 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

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 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 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 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 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 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 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 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 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 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

Introduction

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Acceleration and Newtons Second Law of Motion

Motion With Constant Acceleration

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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 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 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?

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 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 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 $^{\circ}$ ?