Q: A disk is spinning at 7200 rpm. What is its angular velocity $$\omega in $$radians per second?

$$\omega = 7200 \times \frac{2\pi}{60} = 754\ \text{rad/s}$$

Q: Given a disk spinning at $$\omega = 754\ \text{rad/s}$$ and a radius $$r = 0.03\ \text{m}$$, what is the linear velocity $$v at $$the edge?

$$v = r\omega = 0.03 \times 754 = 22.6\ \text{m/s}$$

Q: A rotor accelerates from rest to 20,000 rpm in 30 seconds with constant angular acceleration. What is the angular acceleration $$\alpha in$$ $$\text{rad/s}^2$$?

$$\alpha = \frac{\omega_f - \omega_i}{t} = \frac{20,000 \times \frac{2\pi}{60}}{30} = 70\ \text{rad/s}^2$$

Q: A wheel starts from rest and accelerates at $$\alpha = 2\ \text{rad/s}^2$$ for 10 seconds. What is its final angular velocity $$\omega$$?

$$\omega = \$$omega_0$$ + \alpha t = 0 + 2 \times 10 = 20\ \text{rad/s}$$

Q: A rotating object has angular velocity $$\omega$$ and angular acceleration $$\alpha. $$Which equation gives the angular displacement $$\theta$$ after time $$t$$?

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

Q: If a force is applied at a point on a door 0.8 m from the hinge, and the force is 10 N perpendicular to the door, what is the torque?

$$\tau = 0.8 \times 10 = 8\ \text{N}\cdot\text{m}$$

Q: Which of the following is the correct formula for the cross product magnitude $$|\vec{R} \times \vec{F}|$$?

$$|\vec{R}| |\vec{F}| \sin\theta$$

Question 1

A disk is spinning at 7200 rpm. What is its angular velocity $$\omega in $$radians per second?

Accepted Answer

$$\omega = 7200 	imes \frac{2\pi}{60} = 754\ 	ext{rad/s}$$

Question 2

Given a disk spinning at $$\omega = 754\ 	ext{rad/s}$$ and a radius $$r = 0.03\ 	ext{m}$$, what is the linear velocity $$v at $$the edge?

Accepted Answer

$$v = r\omega = 0.03 	imes 754 = 22.6\ 	ext{m/s}$$

Question 3

A rotor accelerates from rest to 20,000 rpm in 30 seconds with constant angular acceleration. What is the angular acceleration $$\alpha in$$ $$	ext{rad/s}^2$$?

Accepted Answer

$$\alpha = \frac{\omega_f - \omega_i}{t} = \frac{20,000 	imes \frac{2\pi}{60}}{30} = 70\ 	ext{rad/s}^2$$

Question 4

If a force $$F is $$applied at a distance $$R$$ from the pivot, what is the torque $$	au$$ produced?

Accepted Answer

$$	au = R F \sin	heta$$

Question 5

Which of the following best describes the right-hand rule for determining the direction of angular velocity $$\vec{\omega}$$?

Accepted Answer

Curl the fingers of your right hand in the direction of rotation; your thumb points in the direction of $$\vec{\omega}.$$

Question 6

A force $$F is $$applied perpendicular to a lever arm of length $$R. $$What is the magnitude of the torque?

Accepted Answer

$$	au = R F$$

Question 7

If $$\vec{	au} = \vec{R} 	imes \vec{F}$$, what is the direction of the torque vector relative to $$\vec{R}$$ and $$\vec{F}$$?

Accepted Answer

Perpendicular to the plane formed by $$\vec{R}$$ and $$\vec{F}$$

Question 8

A wheel starts from rest and accelerates at $$\alpha = 2\ 	ext{rad/s}^2$$ for 10 seconds. What is its final angular velocity $$\omega$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t = 0 + 2 	imes 10 = 20\ 	ext{rad/s}$$

Question 9

Which equation correctly relates linear acceleration $$a$$ and angular acceleration $$\alpha$$ for a point at radius $$r$$?

Accepted Answer

$$a = r \alpha$$

Question 10

A force $$F is $$applied at an angle $$	heta to a $$lever arm $$R. $$What is the component of the force that produces torque?

Accepted Answer

$$F \sin	heta$$

Question 11

A rotating object has angular velocity $$\omega$$ and angular acceleration $$\alpha. $$Which equation gives the angular displacement $$	heta$$ after time $$t$$?

Accepted Answer

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

Question 12

If a force is applied at a point on a door 0.8 m from the hinge, and the force is 10 N perpendicular to the door, what is the torque?

Accepted Answer

$$	au = 0.8 	imes 10 = 8\ 	ext{N}\cdot	ext{m}$$

Question 13

Which of the following is the correct rotational analog of Newton's second law?

Accepted Answer

$$	au = I \alpha$$

Question 14

A force $$F is $$applied at a distance $$d_1$$ from the pivot, and another force $$F is $$applied at distance $$d_2 = 0$. What is the net torque?

Accepted Answer

$$	au = F d_1$

Question 15

If $$\vec{R}$$ points east and $$\vec{F}$$ points north, what is the direction of $$\vec{	au} = \vec{R} 	imes \vec{F}$$?

Accepted Answer

Upward (out of the plane)

Question 16

A wheel rotates with constant angular acceleration. Which equation gives the final angular velocity $$\omega$$ after time $$t$$?

Accepted Answer

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

Question 17

Which of the following is the correct formula for the cross product magnitude $$|\vec{R} 	imes \vec{F}|$$?

Accepted Answer

$$|\vec{R}| |\vec{F}| \sin	heta$$

Question 18

A force of 5 N is applied at an angle of $$30^\circ to a $$lever arm of length 2 m. What is the torque produced?

Accepted Answer

$$	au = 2 	imes 5 	imes \sin 30^\circ = 5\ 	ext{N}\cdot	ext{m}$$

Rotational Motion and Torque: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드