Q: A wheel starts from rest and rotates with a constant angular acceleration $$\alpha = 3.00\ \mathrm{$$rad/s^2$$}. If $$its angular speed after $$2.00\ \mathrm{s} is$$ $$2.00\ \mathrm{rad/s}$$, what is the angular displacement $$\Delta \theta$$ during this time?

$$\Delta \theta = 10\ \mathrm{rad}$$

Q: Which of the following statements about angular velocity $$\omega is $$correct?

It is defined as $$\omega = \dfrac{d\theta}{dt}.$$

Q: A rigid object is rotating with constant angular acceleration $$\alpha. $$Which kinematic equation gives the angular displacement $$\theta$$ after time $$t if $$the initial angular velocity is $$\$$omega_0$$?

$$\theta = \$$omega_0$$ t + \dfrac{1}{2} \alpha t^2$

Question 1

A rigid disk rotates about a fixed axis. If a point on the rim of the disk moves through an arc length $$s at a $$radius $$r$$, what is the angular displacement $$	heta in $$radians?

Accepted Answer

$$	heta = \dfrac{s}{r}$$

Question 2

Which of the following best describes the physical meaning of torque ($$	au) in $$rotational motion?

Accepted Answer

The product of force and the perpendicular distance from the axis of rotation

Question 3

A wheel starts from rest and rotates with a constant angular acceleration $$\alpha = 3.00\ \mathrm{$$rad/s^2$$}. If $$its angular speed after $$2.00\ \mathrm{s} is$$ $$2.00\ \mathrm{rad/s}$$, what is the angular displacement $$\Delta 	heta$$ during this time?

Accepted Answer

$$\Delta 	heta = 10\ \mathrm{rad}$$

Question 4

Which of the following statements about angular velocity $$\omega is $$correct?

Accepted Answer

It is defined as $$\omega = \dfrac{d	heta}{dt}.$$

Question 5

A mechanic uses a longer wrench to loosen a tight bolt. Why does the longer wrench make the task easier?

Accepted Answer

It increases the torque by increasing the lever arm.

Question 6

If a force $$F is $$applied tangentially to a wheel of radius $$r$$, what is the resulting torque $$	au$$ about the center?

Accepted Answer

$$	au = Fr$$

Question 7

Which of the following is the correct SI unit for torque?

Accepted Answer

Newton-meter

Question 8

A rotating rod of length $$L$$ and mass $$M$$ pivots about one end. What is the angular acceleration $$\alpha if a $$force due to gravity acts at the center of mass?

Accepted Answer

$$\alpha = \dfrac{3g}{2L}$$

Question 9

Which of the following best describes the right-hand rule for determining the direction of angular velocity?

Accepted Answer

Curl your fingers in the direction of rotation; your thumb points in the direction of angular velocity.

Question 10

A particle moves in a circle of radius $$r$$ under a tangential force $$F_t. $$What is the tangential acceleration $$a_t$$?

Accepted Answer

$$a_t = \dfrac{F_t}{m}$$

Question 11

Which equation correctly relates linear velocity $$v$$ and angular velocity $$\omega$$ for a point at radius $$r$$?

Accepted Answer

$$v = r \omega$$

Question 12

A rigid object is rotating with constant angular acceleration $$\alpha. $$Which kinematic equation gives the angular displacement $$	heta$$ after time $$t if $$the initial angular velocity is $$\$$omega_0$$?

Accepted Answer

$$	heta = \$$omega_0$$ t + \dfrac{1}{2} \alpha t^2$

Question 13

Which of the following is NOT a correct analogy between linear and rotational motion?

Accepted Answer

Force $$F$$ corresponds to angular velocity $$\omega$$

Question 14

If the net torque on a rigid object is zero, what can be concluded about its rotational motion?

Accepted Answer

The object rotates with constant angular velocity.

Question 15

A force $$F is $$applied at an angle $$	heta to a $$lever arm $$r. $$What is the expression for the torque $$	au$$ produced?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 16

Which of the following scenarios demonstrates the use of torque in everyday life?

Accepted Answer

Using a wrench to loosen a bolt

Question 17

If a rotating object’s angular velocity is decreasing in the clockwise direction, what is the sign of its angular acceleration?

Accepted Answer

Positive

Question 18

Which of the following is true about the units of angular acceleration $$\alpha$$?

Accepted Answer

It is measured in radians per second squared ($$\mathrm{$$rad/s^2$$})$$

Question 19

A disk rotates from $$\$$theta_1$$ = 0 to$$ $$\$$theta_2$$ = 2\pi$$ radians in $$4$$ seconds. What is the average angular velocity $$\omega_{avg}$$?

Accepted Answer

$$\omega_{avg} = \dfrac{2\pi}{4} = 0.5\pi\ \mathrm{rad/s}$$

Question 20

Which of the following best explains why torque is not measured in Joules, even though its units are $$\mathrm{N \cdot m}$$?

Accepted Answer

Torque causes rotation, while work is energy transfer.

Rotational Motion: Study Notes for General Physics I

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