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?

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

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?

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 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

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?

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 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?

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

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s2. At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?

A) 0.55 s B) 0.63 s C) 0.69 s D) 0.59 s E) 0.47 s A) 0.55 s B) 0.63 s C) 0.69 s D) 0.59 s E) 0.47 s

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

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 first 12 minutes?

(Multiple Choice)

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Question 41

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?

(Multiple Choice)

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Question 42

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?

(Multiple Choice)

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Question 43

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?

(Multiple Choice)

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Question 44

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° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position?

(Multiple Choice)

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Question 45

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?

(Multiple Choice)

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Question 46

If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.

(Multiple Choice)

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Question 47

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval?

(Multiple Choice)

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Question 48

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?

(Multiple Choice)

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Question 49

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J. What is the moment of inertia of the propeller?

(Short Answer)

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Question 50

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?

(Multiple Choice)

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Question 51

When the center of a bicycle wheel has linear velocity relative to the ground, the velocity relative to the ground of point P' at the top of the wheel is

(Multiple Choice)

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Question 52

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s² starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

(Multiple Choice)

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Question 53

The angular speed of the minute hand of a clock, in rad/s, is

(Multiple Choice)

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Question 54

A rod of length 1.00 m has a mass per unit length given by , where 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?

(Short Answer)

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Question 55

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s². At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?

(Multiple Choice)

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Question 56

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 57

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?

(Multiple Choice)

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Question 58

A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s². At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

(Multiple Choice)

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Question 59

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 first 12 minutes?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 82

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

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 first 12 minutes?

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?

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?

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° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position?

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?

If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J. What is the moment of inertia of the propeller?

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?

When the center of a bicycle wheel has linear velocity relative to the ground, the velocity relative to the ground of point P' at the top of the wheel is

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s2 starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

The angular speed of the minute hand of a clock, in rad/s, is

A rod of length 1.00 m has a mass per unit length given by , where 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?

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?

A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2. At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

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 first 12 minutes?

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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?

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?

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?

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?

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s² starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

A rod of length 1.00 m has a mass per unit length given by , where 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 wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s². At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?