Q: Which equation relates angular displacement ($$\Delta \theta$$), angular velocity ($$\omega$$), and angular acceleration ($$\alpha) $$for constant acceleration?

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

Q: Revolutionaries pull a rope tied to the top of a 17 m statue with a force of 4200 N at an angle of 65° to the horizontal. What is the magnitude of the torque?

$$\tau = 17 \times 4200 \times \sin 65^\circ \approx 64,700\ \text{N}\cdot\text{m}$$

Q: Given three masses: $$m_1 = 1$$\ \text{kg}$$ at (0$$,1)$$, m_2$ = 1\ \text{kg} at$$ $$(0,0)$$, and $$m_3 = 2$$\ \text{kg}$$ at (1$$,0)$$, what is the y-coordinate of the center of gravity?

$$y_{cg} = \frac{1 \times 1 + 1 \times 0 + 2 \times 0}{1 + 1 + 2} = 0.25$$

Question 1

A roulette wheel spins at a constant rate. Which physical quantity best describes its rotational motion?

Accepted Answer

Angular velocity ($$\omega)$$

Question 2

Which statement best describes a rigid body?

Accepted Answer

An object whose size and shape do not change as it moves.

Question 3

In uniform circular motion, what remains constant?

Accepted Answer

The speed and radius of the motion.

Question 4

A high-speed drill speeds up from rest to 2400 rpm in 2.5 s. What is its angular acceleration in $$	ext{rad/s}^2$$?

Accepted Answer

$$16.1\ 	ext{rad/s}^2$$

Question 5

Which equation relates angular displacement ($$\Delta 	heta$$), angular velocity ($$\omega$$), and angular acceleration ($$\alpha) $$for constant acceleration?

Accepted Answer

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

Question 6

What is the torque exerted by a force $$F$$ applied at a distance $$r$$ from the pivot at an angle $$	heta$$?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 7

Revolutionaries pull a rope tied to the top of a 17 m statue with a force of 4200 N at an angle of 65° to the horizontal. What is the magnitude of the torque?

Accepted Answer

$$	au = 17 	imes 4200 	imes \sin 65^\circ \approx 64,700\ 	ext{N}\cdot	ext{m}$$

Question 8

If a torque tends to rotate an object in a counterclockwise direction, how is it classified?

Accepted Answer

Positive torque

Question 9

Which scenario results in zero torque about a pivot point?

Accepted Answer

Force applied directly toward or away from the pivot.

Question 10

A gymnast hangs from a bar. Where does the weight force act to produce a torque?

Accepted Answer

At the gymnast's center of gravity.

Question 11

How do you calculate the x-coordinate of the center of gravity for a system of particles?

Accepted Answer

$$x_{cg} = \frac{x_1$ m_1$ + x_2$ m_2$ + x_3$ m_3$ + \ldots}{m_1$ + m_2$ + m_3$ + \ldots}$$

Question 12

Given three masses: $$m_1 = 1$$\ 	ext{kg}$$ at (0$$,1)$$, m_2$ = 1\ 	ext{kg} at$$ $$(0,0)$$, and $$m_3 = 2$$\ 	ext{kg}$$ at (1$$,0)$$, what is the y-coordinate of the center of gravity?

Accepted Answer

$$y_{cg} = \frac{1 	imes 1 + 1 	imes 0 + 2 	imes 0}{1 + 1 + 2} = 0.25$$

Question 13

Which variable is the angular analog of linear velocity?

Accepted Answer

Angular velocity ($$\omega)$$

Question 14

A door is pushed with a force $$F at a $$distance $$r$$ from the hinge. Which action maximizes the torque?

Accepted Answer

Applying the force perpendicular to the door.

Question 15

If an object rotates clockwise and speeds up, what is the sign of its angular acceleration?

Accepted Answer

Negative

Question 16

Which equation describes the relationship between arc length $$s$$, radius $$r$$, and angular position $$	heta$$?

Accepted Answer

$$s = r 	heta$$

Question 17

A wrench is used to loosen a bolt. Which factor does NOT affect the torque produced?

Accepted Answer

The mass of the wrench.

Question 18

Which of the following best describes the center of gravity?

Accepted Answer

The point where the entire weight of an object acts.

Rotational Kinematics and Torque: Study Notes

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