Question 1

Two vectors lying in the xy plane are given by the equations   and   . The value of   is

Accepted Answer

A)  19
  
B)  −11
  
C)  −19
  
D)  11
  
E)  10
  
A)  19
  
B)  −11
  
C)  −19
  
D)  11
  
E)  10
  C

Question 2

A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision?

Accepted Answer

A)  8.1 
B)  2.0 
C)  6.1 
D)  4.2 
E)  10 
A)  8.1 
B)  2.0 
C)  6.1 
D)  4.2 
E)  10 D

Question 3

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. D

Question 4

A 0.5 kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about

Accepted Answer

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

Question 5

A puck on a frictionless air hockey table has a mass of 5.0 g 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 cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is

Accepted Answer

A)  4.0 
B)  6.0 
C)  12 
D)  2.0 
E)  8.0 
A)  4.0 
B)  6.0 
C)  12 
D)  2.0 
E)  8.0

Question 6

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

Question 7

The diagram below shows five thin cylindrical shells, each shell rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass. Which cylindrical shell has the largest angular momentum?

Accepted Answer

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

Question 8

Two blocks, m1 = 1.0 kg and m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg⋅m2, the acceleration of the system is

Accepted Answer

A)  (1/6)g 
B)  (3/8)g 
C)  (1/8)g 
D)  (1/2)g 
E)  (5/8)g 
A)  (1/6)g 
B)  (3/8)g 
C)  (1/8)g 
D)  (1/2)g 
E)  (5/8)g

Question 9

A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is

Accepted Answer

A)  (2/3)g 
B)  (1/2)g 
C)  (1/3)g 
D)  (1/6)g 
E)  (5/6)g 
A)  (2/3)g 
B)  (1/2)g 
C)  (1/3)g 
D)  (1/6)g 
E)  (5/6)g

Question 10

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 11

A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is   MR2, how far will the coin roll up the inclined plane?

Accepted Answer

Question 12

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

Accepted Answer

A)  (m + M/3)(vL/2) 
B)  (m + M/12)(vL/2) 
C)  (m + M/6)(vL/2) 
D)  mvL/2 
E)  mvL 
A)  (m + M/3)(vL/2) 
B)  (m + M/12)(vL/2) 
C)  (m + M/6)(vL/2) 
D)  mvL/2 
E)  mvL

Question 13

A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess?

Accepted Answer

A)  clockwise 
B)  counterclockwise 
C)  It's random, if it starts clockwise it will continue clockwise, and vice versa, i.e., a 50% chance either way. 
D)  The direction depends on the little shove given to the axis when the top is placed on the surface. 
E)  In the northern hemisphere it will be clockwise, in the southern hemisphere it will be counterclockwise. 
A)  clockwise 
B)  counterclockwise 
C)  It's random, if it starts clockwise it will continue clockwise, and vice versa, i.e., a 50% chance either way. 
D)  The direction depends on the little shove given to the axis when the top is placed on the surface. 
E)  In the northern hemisphere it will be clockwise, in the southern hemisphere it will be counterclockwise.

Question 14

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 15

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 16

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque?

Accepted Answer

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

Question 17

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 18

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 19

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Accepted Answer

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

Question 20

Two vectors lying in the xz plane are given by the equations   and   . The value of   is

Accepted Answer

A) 
  
B) 
  
C)  7
  
D)  −7
  
E) 
  
A) 
  
B) 
  
C)  7
  
D)  −7
  
E)

Exam 11: Angular Momentum

Two vectors lying in the xy plane are given by the equations and . The value of is

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 0.5 kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about

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

Two blocks, m1 = 1.0 kg and m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg⋅m2, the acceleration of the system is

A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is

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

A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is MR2, how far will the coin roll up the inclined plane?

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess?

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

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque?

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?

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Two vectors lying in the xz plane are given by the equations and . The value of is

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Two blocks, m₁ = 1.0 kg and m₂ = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg⋅m², the acceleration of the system is

A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is MR², how far will the coin roll up the inclined plane?

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?