Question 1

A solid cylinder rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

Accepted Answer

A) (5/7)g sin θ 
B) (1/2)g sin θ 
C) (2/3)g sin θ 
D) (3/5)g sin θ 
E) (4/5)g sin θ 
A) (5/7)g sin θ 
B) (1/2)g sin θ 
C) (2/3)g sin θ 
D) (3/5)g sin θ 
E) (4/5)g sin θ C

Question 2

A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m.What is the magnitude of its angular momentum (in kg⋅m2/s)relative to the center of the race track?

Accepted Answer

A) 5.0 × 102 
B) 5.0 × 106 
C) 2.5 × 104 
D) 2.5 × 106 
E) 5.0 × 103 
A) 5.0 × 102 
B) 5.0 × 106 
C) 2.5 × 104 
D) 2.5 × 106 
E) 5.0 × 103 B

Question 3

A particle located at the position vector  
M has a force  
N acting on it.The torque about the origin is

Accepted Answer

A) (1   )N⋅m 
B) (5   )N⋅m 
C) (−1   )N⋅m 
D) (−5   )N⋅m 
E) (2   + 3   )N⋅m 
A) (1   )N⋅m 
B) (5   )N⋅m 
C) (−1   )N⋅m 
D) (−5   )N⋅m 
E) (2   + 3   )N⋅m A

Question 4

Exhibit 11-1
Two blocks of masses mS1U1B11S1U1B0 and mS1U1B12S1U1B0 are connected by a light cord that passes over a pulley of mass M,as shown.Block mS1U1B12S1U1B0 slides on a frictionless horizontal surface.The blocks and pulley are initially at rest.When mS1U1B11S1U1B0 is released,the blocks accelerate and the pulley rotates.The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is   Use this exhibit to answer the following question(s).
-Refer to Exhibit 11-1.The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is

Accepted Answer

A) proportional to the radius of the pulley. 
B) proportional to the speed of the blocks. 
C) proportional to the length of the string. 
D) to all of the above. 
E) only to (a)and (b)above. 
A) proportional to the radius of the pulley. 
B) proportional to the speed of the blocks. 
C) proportional to the length of the string. 
D) to all of the above. 
E) only to (a)and (b)above.

Question 5

The object shown below has mass m and velocity  
)The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is

Accepted Answer

A) downwards. 
B) to the right. 
C) into the page. 
D) up out of the page. 
E) counterclockwise. 
A) downwards. 
B) to the right. 
C) into the page. 
D) up out of the page. 
E) counterclockwise.

Question 6

A cylindrical shell rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

Accepted Answer

A) (5/7)g sin θ 
B) (1/2)g sin θ 
C) (3/5)g sin θ 
D) (2/3)g sin θ 
E) (4/5)g sin θ 
A) (5/7)g sin θ 
B) (1/2)g sin θ 
C) (3/5)g sin θ 
D) (2/3)g sin θ 
E) (4/5)g sin θ

Question 7

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The angular momentum of the puck (in kg⋅m2/s)is

Accepted Answer

A) 80 
B) 20 
C) 30 
D) 60 
E) 50 
A) 80 
B) 20 
C) 30 
D) 60 
E) 50

Question 8

A force  
Is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown.The acceleration of the center of mass of the roll of paper (when it rolls without slipping)is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 9

A 3.0-kg particle has a position vector given by  
Where  
Is in meters and t is in seconds.What is the angular momentum of the particle,in kg⋅m2/s,about the origin at t = 2 s?

Accepted Answer

A) 72   
B) −72   
C) 24   
D) −24   
E) 22   
A) 72   
B) −72   
C) 24   
D) −24   
E) 22

Question 10

What is the angular momentum of the moon about the Earth? The mass of the moon is 7.35 × 1022 kg,the center-to-center separation of the Earth and the moon is 3.84 × 105 km,and the orbital period of the moon is 27.3 days.Ignore the small offset of the center of mass of the system from the center of the Earth in your calculation.

Accepted Answer

Question 11

A space station out beyond the solar system is rotating with constant angular velocity.A spaceship heading into the station along a diameter of the station,uses its rockets to brake,and then docks inside the station at its center.When the spaceship docks,the angular momentum of the system consisting of the station and ship

Accepted Answer

A) is less than the original angular momentum of the station. 
B) is the same as the original angular momentum of the station. 
C) is greater than the original angular momentum of the station. 
D) is less than the original angular momentum of the station,but the angular velocity increases. 
E) is greater than the original angular momentum of the station,but the angular velocity decreases. 
A) is less than the original angular momentum of the station. 
B) is the same as the original angular momentum of the station. 
C) is greater than the original angular momentum of the station. 
D) is less than the original angular momentum of the station,but the angular velocity increases. 
E) is greater than the original angular momentum of the station,but the angular velocity decreases.

Question 12

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end.In this collision

Accepted Answer

A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved. 
A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved.

Question 13

A torque can be exerted on a body with a fixed axis of rotation

Accepted Answer

A) only by a centripetal force. 
B) only by a force directed radially outwards. 
C) only by a tangential force. 
D) only by a force with a component directed radially outwards. 
E) by any force not pointing directly toward or away from the axis of rotation. 
A) only by a centripetal force. 
B) only by a force directed radially outwards. 
C) only by a tangential force. 
D) only by a force with a component directed radially outwards. 
E) by any force not pointing directly toward or away from the axis of rotation.

Question 14

A solid sphere,spherical shell,solid cylinder and a cylindrical shell all have the same mass m and radius R.If they are all released from rest at the same elevation and roll without slipping,which reaches the bottom of an inclined plane first?

Accepted Answer

A) solid sphere 
B) spherical shell 
C) solid cylinder 
D) cylindrical shell 
E) all take the same time 
A) solid sphere 
B) spherical shell 
C) solid cylinder 
D) cylindrical shell 
E) all take the same time

Question 15

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg⋅m2/s)relative to the origin?

Accepted Answer

A) −30   
B) 30   
C) −15   
D) 15   
E) 45   
A) −30   
B) 30   
C) −15   
D) 15   
E) 45

Question 16

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice.In this collision

Accepted Answer

A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved. 
A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved.

Question 17

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅m2,and is rotating at 10 rpm.A child whose mass is 25 kg jumps onto the edge of the merry-go-round,heading directly toward the center at 6.0 m/s.The new angular speed (in rpm)of the merry-go-round is approximately

Accepted Answer

A) 10 
B) 9.2 
C) 8.5 
D) 7.1 
E) 6.4 
A) 10 
B) 9.2 
C) 8.5 
D) 7.1 
E) 6.4

Question 18

Exhibit 11-1
Two blocks of masses mS1U1B11S1U1B0 and mS1U1B12S1U1B0 are connected by a light cord that passes over a pulley of mass M,as shown.Block mS1U1B12S1U1B0 slides on a frictionless horizontal surface.The blocks and pulley are initially at rest.When mS1U1B11S1U1B0 is released,the blocks accelerate and the pulley rotates.The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is   Use this exhibit to answer the following question(s).
-Refer to Exhibit 11-1.The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is

Accepted Answer

A) the same at all times. 
B) proportional to l1,the length of string from the pulley to m1. 
C) proportional to l2,the length of string from the pulley to m2. 
D) conserved because the Earth doesn't move. 
E) proportional to the speed of the blocks. 
A) the same at all times. 
B) proportional to l1,the length of string from the pulley to m1. 
C) proportional to l2,the length of string from the pulley to m2. 
D) conserved because the Earth doesn't move. 
E) proportional to the speed of the blocks.

Question 19

When an object is effectively isolated from external torques,like an ice skater twirling on the tip of one skate,the angular momentum of the object

Accepted Answer

A) can be increased by shifting mass out away from the axis of rotation. 
B) can be decreased by shifting mass out away from the axis of rotation. 
C) can be increased by shifting mass in toward the axis of rotation. 
D) can be decreased by shifting mass in toward the axis of rotation. 
E) cannot be changed except by friction at the point of contact. 
A) can be increased by shifting mass out away from the axis of rotation. 
B) can be decreased by shifting mass out away from the axis of rotation. 
C) can be increased by shifting mass in toward the axis of rotation. 
D) can be decreased by shifting mass in toward the axis of rotation. 
E) cannot be changed except by friction at the point of contact.

Question 20

Five objects of mass m move at velocity  
At a distance r from an axis of rotation perpendicular to the page through point A,as shown below.The one that has zero angular momentum about that axis is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Exam 11: Angular Momentum

A solid cylinder rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m.What is the magnitude of its angular momentum (in kg⋅m2/s)relative to the center of the race track?

A particle located at the position vector M has a force N acting on it.The torque about the origin is

The object shown below has mass m and velocity )The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is

A cylindrical shell rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The angular momentum of the puck (in kg⋅m2/s)is

A force Is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown.The acceleration of the center of mass of the roll of paper (when it rolls without slipping)is

A 3.0-kg particle has a position vector given by Where Is in meters and t is in seconds.What is the angular momentum of the particle,in kg⋅m2/s,about the origin at t = 2 s?

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end.In this collision

A torque can be exerted on a body with a fixed axis of rotation

A solid sphere,spherical shell,solid cylinder and a cylindrical shell all have the same mass m and radius R.If they are all released from rest at the same elevation and roll without slipping,which reaches the bottom of an inclined plane first?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg⋅m2/s)relative to the origin?

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice.In this collision

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅m2,and is rotating at 10 rpm.A child whose mass is 25 kg jumps onto the edge of the merry-go-round,heading directly toward the center at 6.0 m/s.The new angular speed (in rpm)of the merry-go-round is approximately

When an object is effectively isolated from external torques,like an ice skater twirling on the tip of one skate,the angular momentum of the object

Five objects of mass m move at velocity At a distance r from an axis of rotation perpendicular to the page through point A,as shown below.The one that has zero angular momentum about that axis is

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A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m.What is the magnitude of its angular momentum (in kg⋅m²/s)relative to the center of the race track?

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The angular momentum of the puck (in kg⋅m²/s)is

A 3.0-kg particle has a position vector given by Where Is in meters and t is in seconds.What is the angular momentum of the particle,in kg⋅m²/s,about the origin at t = 2 s?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg⋅m²/s)relative to the origin?

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅m²,and is rotating at 10 rpm.A child whose mass is 25 kg jumps onto the edge of the merry-go-round,heading directly toward the center at 6.0 m/s.The new angular speed (in rpm)of the merry-go-round is approximately