Question 1

A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?

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Question 2

A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg∙m², and the wheel slows to a stop in 160 s, what is the magnitude of the retarding torque?

Accepted Answer

The retarding torque can be calculated using the formula: torque = I * alpha, where alpha is the angular deceleration. First, find alpha using the formula: alpha = (final angular speed - initial angular speed) / time = (0 - 12.0 rad/s) / 160 s = -0.075 rad/s². Then, torque = 0.100 kg∙m² * 0.075 rad/s² = 0.00750 Nm.

Question 3

FIGURE 11-4 -The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m₁, m₂, and m₃?

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-The mobile shown in Figure...

Question 4

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

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Question 5

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is held at 30.0° below the horizontal?

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Question 6

A ball with diameter 10. cm rolls without slipping on a horizontal table top. The moment of inertia of the ball is 2.2 × 10^-3 kg- m² and its translational speed is 0.45 m/s. (a) What is its angular speed about its center of mass? (b) What is its rotational kinetic energy? (c) What is its angular momentum?

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Question 7

A horizontal 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N forces pushes downward. At the west end of the beam, a 200-N force pushed upward. What is the angular acceleration of the beam?

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Question 8

In a lab experiment, a student brings up the rotational speed of a rotational motion apparatus to 30.0 rpm. She then allows the apparatus to slow down on its own, and counts 240 revolutions before the apparatus comes to a stop. The moment of inertia of the flywheel is 0.0850 kg∙m². What is the retarding torque on the flywheel?

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Question 9

Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

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Question 10

A 82.0 kg painter stands on a long horizontal board 1.55 m from one end. The 15.5 kg board is 5.50 m long. The board is supported at each end.
(a) What is the total force provided by both supports?
(b) With what force does the support, closest to the painter, push upward?

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The answer of A 82.0 kg painter stands on a...

Question 11

A horizontal, 2.00 m long, 3.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam?

Accepted Answer

The answer of A horizontal, 2.00 m long, 3.00 kg...

Question 12

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg∙m². What is the angular acceleration of the wheel?

Accepted Answer

The answer of The drive chain in a bicycle is...

Question 13

A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. A second weight, with a weight of 15 N, is placed on the far end from the board. What forces are exerted by the sawhorses on the board?

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Question 14

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-  and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

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Question 15

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

Accepted Answer

The torque applied to the wheel is given by:$$ au = I \alpha$$where:$$ au$$ is the torque$$I$$ is the moment of inertia$$\alpha$$ is the angular accelerationThe moment of inertia of a hoop is given by:$$I = MR^2$$where:$$M$$ is the mass$$R$$ is the radiusSubstituting the given values into the equations, we get:$$0.850 ext{ Nm} = (0.750 ext{ kg})(0.330 ext{ m})^2 \alpha$$$$\alpha = 10.4 ext{ rad/s}^2$$Therefore, the angular acceleration of the wheel is 10.4 rad/s².

Question 16

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What force, applied 0.300 m on the other side of the pivot, is needed to make the child lift off the ground?

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Question 17

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

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Question 18

A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3 m from the girl. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight?
 Neglect the weight of the seesaw.

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Question 19

A diver can change her rate of rotation in the air by "tucking" her head in and bending her knees. Let's assume that when she is stretched out straight she is rotating at 1 revolution per second. Now she goes into the "tuck and bend," effectively shortening the length of her body by half. What will her rate of rotation be now?

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Question 20

A 1.8 kg solid disk pulley of radius 0.11 m rotates about an axis through its center.
(a) What is its moment of inertia?
(b) Starting from rest, a torque of 0.22 m-N will produce what angular acceleration?

Accepted Answer

The answer of A 1.8 kg solid disk pulley of...

Quiz 11: Rotational Dynamics and Static Equilibrium

A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?

FIGURE 11-4 -The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m1, m2, and m3?

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is held at 30.0° below the horizontal?

A horizontal 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N forces pushes downward. At the west end of the beam, a 200-N force pushed upward. What is the angular acceleration of the beam?

Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

A 82.0 kg painter stands on a long horizontal board 1.55 m from one end. The 15.5 kg board is 5.50 m long. The board is supported at each end. (a) What is the total force provided by both supports? (b) With what force does the support, closest to the painter, push upward?

A horizontal, 2.00 m long, 3.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam?

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg∙m2. What is the angular acceleration of the wheel?

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg- and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What force, applied 0.300 m on the other side of the pivot, is needed to make the child lift off the ground?

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3 m from the girl. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight? Neglect the weight of the seesaw.

A 1.8 kg solid disk pulley of radius 0.11 m rotates about an axis through its center. (a) What is its moment of inertia? (b) Starting from rest, a torque of 0.22 m-N will produce what angular acceleration?

FIGURE 11-4 -The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m₁, m₂, and m₃?

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg∙m². What is the angular acceleration of the wheel?