Q: A cyclist accelerates from rest, and the wheels of the bicycle rotate with a constant angular acceleration. If the initial angular velocity is zero, which equation correctly describes the angular displacement $$\theta$$ after time $$t$$?

$$\theta = \frac{1}{2} \alpha t^2$

Q: A mechanic uses a wrench to loosen a bolt. The force applied is 200 N at the end of a 0.5 m wrench, perpendicular to the wrench. What is the magnitude of the torque produced?

$$\tau = 100 \text{ N} \cdot \text{m}$$

Q: A plumber stands on the end of a cheater bar, applying a force of 900 N at a distance of 0.80 m from the pivot, at an angle of $$19^\circ$$ with the horizontal. What is the magnitude of the torque about the pivot?

$$\tau = 900 \times 0.80 \times \sin(19^\circ)$$

Question 1

A cyclist accelerates from rest, and the wheels of the bicycle rotate with a constant angular acceleration. If the initial angular velocity is zero, which equation correctly describes the angular displacement $$	heta$$ after time $$t$$?

Accepted Answer

$$	heta = \frac{1}{2} \alpha t^2$

Question 2

A mechanic uses a wrench to loosen a bolt. The force applied is 200 N at the end of a 0.5 m wrench, perpendicular to the wrench. What is the magnitude of the torque produced?

Accepted Answer

$$	au = 100 	ext{ N} \cdot 	ext{m}$$

Question 3

Which of the following best describes the relationship between linear velocity $$v$$ and angular velocity $$\omega$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = \omega r$$

Question 4

A solid cylinder and a hollow cylinder of equal mass and radius are released from rest at the top of an incline. Which will reach the bottom first, and why?

Accepted Answer

The solid cylinder, because it has less rotational inertia.

Question 5

A plumber stands on the end of a cheater bar, applying a force of 900 N at a distance of 0.80 m from the pivot, at an angle of $$19^\circ$$ with the horizontal. What is the magnitude of the torque about the pivot?

Accepted Answer

$$	au = 900 	imes 0.80 	imes \sin(19^\circ)$$

Question 6

Which force orientation is most effective for opening a door, assuming all forces have the same magnitude?

Accepted Answer

A force applied perpendicular to the door at the farthest point from the hinge.

Question 7

A disk rotates with constant angular acceleration. If its initial angular velocity is $$\$$omega_0$$ and angular acceleration is $$\alpha$$, what is its angular velocity $$\omega$$ after time t$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 8

A jar lid is difficult to open. Which action increases the torque applied to the lid?

Accepted Answer

Applying a greater force at the same distance from the center.

Question 9

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$\phi$$ with the moment arm. Which formula gives the torque?

Accepted Answer

$$	au = F r \sin \phi$$

Question 10

A rotating rigid body has a moment of inertia $$I$$ and angular acceleration $$\alpha. $$What is the net torque $$	au_{net}$$ acting on it?

Accepted Answer

$$	au_{net} = I \alpha$$

Question 11

A solid sphere, a solid cylinder, and a thin-walled hollow cylinder of equal mass and radius roll down an incline. Which arrives first and why?

Accepted Answer

Solid sphere, because it has the smallest moment of inertia relative to mass and radius.

Question 12

If a force is applied radially toward the axis of rotation, what is the resulting torque?

Accepted Answer

Zero, because the moment arm is zero.

Question 13

A bicycle crank is acted upon by four forces. Which force does NOT contribute to the net torque?

Accepted Answer

The force applied at the axle.

Question 14

A rigid body rotates about a fixed axis. Which component of force contributes to the torque?

Accepted Answer

The tangential component.

Question 15

A disk of mass $$M$$ and radius $$R$$ rotates about its center. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2} M R^2$

Question 16

A force $$F is $$applied at a distance $$r$$ from the axis of rotation. If the force is not perpendicular to $$r$$, how do you calculate the torque?

Accepted Answer

$$	au = F r \sin \phi$$

Question 17

A hollow cylinder, a solid cylinder, and a hollow cylinder with force applied at its inner radius are shown. Which has the smallest angular acceleration when the same force is applied?

Accepted Answer

The hollow cylinder with force applied at its inner radius.

Question 18

A rotating object slows down with a constant angular acceleration. Which equation describes the angular velocity after time $$t$$?

Accepted Answer

$$\omega = \$$omega_0$$ - \alpha t$$

Question 19

A force is applied to a wrench at an angle. Which component of the force is responsible for producing torque?

Accepted Answer

The component perpendicular to the wrench.

Dynamics of Rotational Motion: Torque, Angular Acceleration, and Applications

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