Q: A particle moves along a circular path of radius $$r = 2.0\ \mathrm{m}$$ and travels an arc length $$s = 3.14\ \mathrm{m}. $$What is the angular position $$\theta (in $$radians) of the particle relative to the positive x-axis?

$$\theta = 3.14\ \mathrm{rad}$$

Q: A force of $$200\ \mathrm{N} is $$applied perpendicular to a door $$0.8\ \mathrm{m}$$ from the hinge. What is the torque $$\tau$$ produced?

$$\tau = 160\ \mathrm{N \cdot m}$$

Q: A 3.0 kg flagpole is attached to a wall at an angle of $$30^\circ$$ above the horizontal. Its center of gravity is $$2.0\ \mathrm{m}$$ from the wall. What is the magnitude of the gravitational torque about the attachment point? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$\tau = (2.0\ \mathrm{m})(3.0\ \mathrm{kg})(9.8\ \mathrm{m/s^2$})\cos 30^\circ = 50.9\ \mathrm{N \cdot m}$$

Q: A solid cylinder (mass $$M$$, radius $$R) is $$rotated about its center by a constant torque $$\tau. $$What is its angular acceleration $$\alpha$$?

$$\alpha = \frac{2\tau}{MR^2$}$$

Question 1

A particle moves along a circular path of radius $$r = 2.0\ \mathrm{m}$$ and travels an arc length $$s = 3.14\ \mathrm{m}. $$What is the angular position $$	heta (in $$radians) of the particle relative to the positive x-axis?

Accepted Answer

$$	heta = 3.14\ \mathrm{rad}$$

Question 2

A wind turbine blade is 40 m long and rotates at 12 rpm. What is the speed $$v of $$the tip of the blade? (Use $$v = \omega r$$ and $$\omega = 2\pi f$$ with $$f in $$rev/s.)

Accepted Answer

$$v = 50.3\ \mathrm{m/s}$$

Question 3

A merry-go-round spins at a constant angular velocity. Sofia sits twice as far from the axis as Rasheed. Compared to Rasheed, Sofia’s speed is:

Accepted Answer

Twice as much

Question 4

A crankshaft in a car engine turns at 3600 rpm. What is its angular speed $$\omega in $$rad/s?

Accepted Answer

$$\omega = 377\ \mathrm{rad/s}$$

Question 5

A force of $$200\ \mathrm{N} is $$applied perpendicular to a door $$0.8\ \mathrm{m}$$ from the hinge. What is the torque $$	au$$ produced?

Accepted Answer

$$	au = 160\ \mathrm{N \cdot m}$$

Question 6

A uniform rod of mass $$M$$ and length $$L$$ rotates about its center. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 7

A wheel starts from rest and undergoes a constant angular acceleration of $$2\ \mathrm{$$rad/s^2$$}. $$What is its angular velocity after $$5\ \mathrm{s}$$?

Accepted Answer

$$\omega = 10\ \mathrm{rad/s}$$

Question 8

A 3.0 kg flagpole is attached to a wall at an angle of $$30^\circ$$ above the horizontal. Its center of gravity is $$2.0\ \mathrm{m}$$ from the wall. What is the magnitude of the gravitational torque about the attachment point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$	au = (2.0\ \mathrm{m})(3.0\ \mathrm{kg})(9.8\ \mathrm{m/s^2$})\cos 30^\circ = 50.9\ \mathrm{N \cdot m}$$

Question 9

A solid cylinder (mass $$M$$, radius $$R) is $$rotated about its center by a constant torque $$	au. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{2	au}{MR^2$}$$

Question 10

A uniform seesaw of mass $$2.0\ \mathrm{kg} is $$balanced by a $$30\ \mathrm{kg}$$ child sitting $$2.5\ \mathrm{m}$$ from the pivot. Where should a $$25\ \mathrm{kg}$$ child sit to balance the seesaw?

Accepted Answer

$$x = 3.0\ \mathrm{m}$$

Question 11

A wheel of radius $$0.5\ \mathrm{m}$$ rolls without slipping at $$v = 4\ \mathrm{m/s}. $$What is its angular velocity $$\omega$$?

Accepted Answer

$$\omega = 8\ \mathrm{rad/s}$$

Question 12

A force $$F is $$applied at an angle $$\phi to a $$wrench of length $$r. $$What is the torque $$	au$$ about the pivot?

Accepted Answer

$$	au = rF\sin \phi$$

Question 13

A wheel starts from rest and turns through $$\Delta 	heta = 25\ \mathrm{rad} in $$time $$t$$ under constant angular acceleration. How far does it turn in time $$2t$$?

Accepted Answer

$$100\ \mathrm{rad}$$

Question 14

A 2.5 kg bucket is attached to a rope wound around a 3.0 kg, 4.0-cm-radius cylinder. If the bucket is released from rest, which statement is true about the acceleration of the bucket?

Accepted Answer

It is less than $$g$$ because some force accelerates the cylinder’s rotation.

Question 15

A solid sphere (mass $$M$$, radius $$R) $$rotates about its diameter. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 16

A fan blade is slowing down while rotating counterclockwise. What are the signs of $$\omega$$ and $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative.

Chapter 7: Rotational Motion – Physics with Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards