Question 1

A uniform rod is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at the horizontal position.What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

Accepted Answer

A)  3.7 rad/s2
B)  1.3 rad/s2
C)  2.5 rad/s2
D)  4.9 rad/s2
E)  1.9 rad/s2

Question 2

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are positive,its angular velocity is positive,and its angular acceleration is negative.The sphere is

Accepted Answer

A)  rotating clockwise and slowing down.
B)  rotating counterclockwise and slowing down.
C)  rotating clockwise and speeding up.
D)  rotating counterclockwise and speeding up.
E)  first rotating clockwise and then counterclockwise.

Question 3

A wheel (radius = 0.25 m) is mounted on a frictionless,horizontal axis.The moment of inertia of the wheel about the axis is 0.040 kg⋅m2.A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure.The object is released from rest.What is the magnitude of the acceleration of the 0.50-kg object? 2.A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure.The object is released from rest.What is the magnitude of the acceleration of the 0.50-kg object?   A) 3.0 m/s2 B) 3.4 m/s2 C) 4.3 m/s2 D) 3.8 m/s2 E) 2.7 m/s2 " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)  3.0 m/s2
B)  3.4 m/s2
C)  4.3 m/s2
D)  3.8 m/s2
E)  2.7 m/s2

Question 4

A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t3,where θ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Accepted Answer

A)  −1.0 rad/s2
B)  −24 rad/s2
C)  −2.0 rad/s2
D)  −4.0 rad/s2
E)  −3.5 rad/s2

Question 5

Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?

Accepted Answer

A)  t = 0.
B)  t =  .
C)  t =  .
D)  t =  .
E)  t =  .

Question 6

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides?

Accepted Answer

A)  2.7 kg⋅m2
B)  3.6 kg⋅m2
C)  3.1 kg⋅m2
D)  4.1 kg⋅m2
E)  1.6 kg⋅m2

Question 7

The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.

Accepted Answer

A)  1.3 rad/s
B)  1.5 rad/s
C)  1.7 rad/s
D)  1.2 rad/s
E)  2.1 rad/s

Question 8

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

Accepted Answer

A)  2.9 J
B)  2.6 J
C)  3.1 J
D)  3.4 J
E)  1.6 J

Question 9

Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass.This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick.If this body is released from rest in a horizontal position,what is the angular speed of the meter stick as it swings through its lowest position?

Accepted Answer

A)  4.2 rad/s
B)  5.4 rad/s
C)  4.6 rad/s
D)  5.0 rad/s
E)  1.7 rad/s

Question 10

A thin uniform rod (length = 1.2 m,mass = 2.0 kg) is pivoted about a horizontal,frictionless pin through one end of the rod.(The moment of inertia of the rod about this axis is ML2/3. ) The rod is released when it makes an angle of 37° with the horizontal.What is the angular acceleration of the rod at the instant it is released?

Accepted Answer

A)  9.8 rad/s2
B)  7.4 rad/s2
C)  8.4 rad/s2
D)  5.9 rad/s2
E)  6.5 rad/s2

Question 11

When a wheel is rolling without slipping,the magnitude of its velocity relative to the ground is greatest at

Accepted Answer

A)  the point in contact with the ground.
B)  the point at the center of the wheel.
C)  the point at the top of the wheel opposite to the point in contact with the ground.
D)  the point farthest forward from the center of mass of the wheel.
E)  the point farthest behind the center of mass of the wheel.

Question 12

A nonuniform 2.0-kg rod is 2.0 m long.The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod.The moment of inertia of the rod about this axis is 4.0 kg⋅m2.The center of mass of the rod is 1.2 m from the axis.If the rod is released from rest in the horizontal position,what is its angular speed as it swings through the vertical position?

Accepted Answer

A)  3.4 rad/s
B)  4.4 rad/s
C)  4.3 rad/s
D)  5.8 rad/s
E)  6.8 rad/s

Question 13

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee.Ignoring air resistance,the torque exerted about its center of mass by gravity is

Accepted Answer

A)  0.
B)  mgr.
C)  2mgr.
D)  a function of the angular velocity.
E)  small at first,then increasing as the Frisbee loses the torque given it by your hand.

Question 14

Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s) .
-Refer to Exhibit 10-1.What is her angular displacement (in rad) in the 16 minute period shown in the graph?

Accepted Answer

A)  0
B)  16π
C)  32π
D)  40π
E)  64π

Question 15

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

Accepted Answer

A)  4.9 rad
B)  4.7 rad
C)  4.5 rad
D)  4.3 rad
E)  4.1 rad

Question 16

A mass (M1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m) rotates about a frictionless axle.The acceleration of M2 is 3.5 m/s2.What is the moment of inertia of the pulley? 1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m) rotates about a frictionless axle.The acceleration of M2 is 3.5 m/s2.What is the moment of inertia of the pulley?   A) 0.29 kg⋅m2 B) 0.42 kg⋅m2 C) 0.20 kg⋅m2 D) 0.62 kg⋅m2 E) 0.60 kg⋅m2 " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)  0.29 kg⋅m2
B)  0.42 kg⋅m2
C)  0.20 kg⋅m2
D)  0.62 kg⋅m2
E)  0.60 kg⋅m2

Question 17

A celestial object called a pulsar emits its light in short bursts that are synchronized with its rotation.A pulsar in the Crab Nebula is rotating at a rate of 30 revolutions/second.What is the maximum radius of the pulsar,if no part of its surface can move faster than the speed of light (3 × 108 m/s)?

Accepted Answer

Question 18

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Accepted Answer

A)  9.5 rad/s
B)  9.7 rad/s
C)  9.3 rad/s
D)  9.1 rad/s
E)  8.8 rad/s

Question 19

A campus bird spots a member of an opposing football team in an amusement park.The football player is on a ride where he goes around at angular velocity ω at distance R from the center.The bird flies in a horizontal circle above him.Will a dropping the bird releases while flying directly above the person's head hit him?

Accepted Answer

A)  Yes,because it falls straight down.
B)  Yes,because it maintains the acceleration of the bird as it falls.
C)  No,because it falls straight down and will land behind the person.
D)  Yes,because it maintains the angular velocity of the bird as it falls.
E)  No,because it maintains the tangential velocity the bird had at the instant it started falling.

Question 20

Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s) .
-Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Accepted Answer

A)  8
B)  12
C)  16
D)  20
E)  40

Exam 10: Rotation of a Rigid Object About a Fixed Axis

A uniform rod is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at the horizontal position.What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

Correct Answer
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Correct Answer
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Correct Answer
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A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t³,where θ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Correct Answer
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Correct Answer
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The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

Correct Answer
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Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?

Correct Answer
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You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee.Ignoring air resistance,the torque exerted about its center of mass by gravity is

Correct Answer
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When a wheel is rolling without slipping,the magnitude of its velocity relative to the ground is greatest at

Correct Answer
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At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the 16 minute period shown in the graph?

Correct Answer
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A mass (M₁ = 5.0 kg) is connected by a light cord to a mass (M₂ = 4.0 kg) which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m) rotates about a frictionless axle.The acceleration of M₂ is 3.5 m/s².What is the moment of inertia of the pulley?

Correct Answer
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Correct Answer
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A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Correct Answer
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Correct Answer
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Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Correct Answer
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Exam 10: Rotation of a Rigid Object About a Fixed Axis

A uniform rod is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at the horizontal position.What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t3,where θ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

Correct AnswerverifiedShow Answer

Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?

Correct AnswerverifiedShow Answer

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee.Ignoring air resistance,the torque exerted about its center of mass by gravity is

Correct AnswerverifiedShow Answer

When a wheel is rolling without slipping,the magnitude of its velocity relative to the ground is greatest at

Correct AnswerverifiedShow Answer

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the 16 minute period shown in the graph?

Correct AnswerverifiedShow Answer

A mass (M1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m) rotates about a frictionless axle.The acceleration of M2 is 3.5 m/s2.What is the moment of inertia of the pulley?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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Correct Answer
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A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t³,where θ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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A mass (M₁ = 5.0 kg) is connected by a light cord to a mass (M₂ = 4.0 kg) which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m) rotates about a frictionless axle.The acceleration of M₂ is 3.5 m/s².What is the moment of inertia of the pulley?

Correct Answer
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Correct Answer
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A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Correct Answer
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Correct Answer
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Correct Answer
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