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$\degree$ with the horizontal.What is the angular acceleration of the rod at the instant it is released?

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 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

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?

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 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

Exam 10: Rotational Motion

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is

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Question 81

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

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Question 82

A wheel (radius = 12 cm)is mounted on a frictionless,horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel.A light cord wrapped around the wheel supports a 0.40-kg object.If released from rest with the string taut,the object is observed to fall with a downward acceleration of 3.0 m/s².What is the moment of inertia (of the wheel)about the given axle?

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Question 83

A rod of length 1.00 m has a mass per unit length given by $\lambda = 2.00 + 1.00 x ^ { 2 }$ ,where $\lambda$ is in kg/m.The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m.What is the moment of inertia of the rod in kg . m² about the y axis?

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Question 84

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

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Question 85

Exhibit 11-1 Two blocks of masses m₁ and m₂ are connected by a light cord that passes over a pulley of mass M,as shown.Block m₂ slides on a frictionless horizontal surface.The blocks and pulley are initially at rest.When m₁ 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

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Question 86

A uniform rod is 3.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 27 $\degree$ above the horizontal.What is the angular speed of the rod as it passes through the horizontal position?

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Question 87

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

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Question 88

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?

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Question 89

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 $\degree$ with the horizontal.What is the angular acceleration of the rod at the instant it is released?

(Multiple Choice)

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Question 90

Five objects of mass m move at velocity $\overrightarrow { \mathbf { v } }$ 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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Question 91

The graph below shows a plot of angular acceleration in rad/s² versus time from t = 0 s to t = 8 s.The angular velocity at t = 0 s is $\omega _ { 0 } = 5 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW.The angular velocity, $\omega$ ,at t = 8 s is $The graph below shows a plot of angular acceleration in rad/s<sup>2</sup> versus time from t = 0 s to t = 8 s.The angular velocity at t = 0 s is \omega _ { 0 } = 5 \frac { \mathrm { rad } } { \mathrm { s } } ,CCW.The angular velocity, \omega ,at t = 8 s is$

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Question 92

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

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Question 93

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?

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Question 94

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s²,in the first 10 minutes?

(Multiple Choice)

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Question 95

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)?

(Short Answer)

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Question 96

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?

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Question 97

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?

(Multiple Choice)

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Question 98

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

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Question 99

A uniform rod (length = 2.4 m)of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end.The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass.The rod is released from rest when it is horizontal.What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point?

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Question 100

Showing 81 - 100 of 121

Exam 10: Rotational Motion

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis 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 rod of length 1.00 m has a mass per unit length given by λ=2.00+1.00x2\lambda = 2.00 + 1.00 x ^ { 2 }λ=2.00+1.00x2 ,where λ\lambdaλ is in kg/m.The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m.What is the moment of inertia of the rod in kg . m2 about the y axis?

A force F→\overrightarrow { \mathrm { F } }F 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 uniform rod is 3.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 27 °\degree° above the horizontal.What is the angular speed of the rod as it passes through the horizontal position?

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?

Five objects of mass m move at velocity v→\overrightarrow { \mathbf { v } }v 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

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The angular velocity at t = 0 s is ω0=5rads\omega _ { 0 } = 5 \frac { \mathrm { rad } } { \mathrm { s } }ω0​=5srad​ ,CCW.The angular velocity, ω \omega ω ,at t = 8 s 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

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?

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 solid cylinder rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass 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 rod of length 1.00 m has a mass per unit length given by $\lambda = 2.00 + 1.00 x ^ { 2 }$ ,where $\lambda$ is in kg/m.The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m.What is the moment of inertia of the rod in kg . m² about the y axis?

A uniform rod is 3.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 27 $\degree$ above the horizontal.What is the angular speed of the rod as it passes through the horizontal position?

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?

Five objects of mass m move at velocity $\overrightarrow { \mathbf { v } }$ 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

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

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s²,in the first 10 minutes?

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?