Q: A 3.2 kg flagpole extends from a wall at an angle of $$25^\circ$$ from the horizontal. Its center of gravity is 1.6 m from the wall. What is the magnitude of the gravitational torque about the attachment point? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\tau = 42.5\ \mathrm{N\cdot m}$$

Q: A force of $$240\ \mathrm{N} is $$applied at $$0.75\ \mathrm{m}$$ from a door hinge at $$20^\circ$$ from perpendicular. What is the torque?

$$\tau = 169\ \mathrm{N\cdot m}$$

Question 1

A wind turbine blade is 50 m long and rotates at 10 rpm. What is the speed $$v of $$the tip of the blade? (Use $$v = r \omega$$ and $$\omega in $$rad/s.)

Accepted Answer

$$v = 52.4\ \mathrm{m/s}$$

Question 2

A merry-go-round rotates 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 Rasheed’s speed

Question 3

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

Accepted Answer

$$I = \frac{1}{3}ML^2$

Question 4

A 3.2 kg flagpole extends from a wall at an angle of $$25^\circ$$ from the horizontal. Its center of gravity is 1.6 m from the wall. What is the magnitude of the gravitational torque about the attachment point? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$	au = 42.5\ \mathrm{N\cdot m}$$

Question 5

A wheel starts from rest and rotates with constant angular acceleration. If it turns through $$25\ \mathrm{rad} in $$time $$t$$, how far will it have turned after time $$2t$$?

Accepted Answer

$$100\ \mathrm{rad}$$

Question 6

A force $$F is $$applied at a distance $$r$$ from a pivot at an angle $$\phi to $$the radial line. What is the torque $$	au$$ produced?

Accepted Answer

$$	au = rF\sin\phi$$

Question 7

A flywheel (solid cylinder) of mass $$540\ \mathrm{kg}$$ and radius $$0.30\ \mathrm{m} is $$spun up by a constant torque of $$120\ \mathrm{N\cdot m}. $$How long does it take to reach $$13,000\ \mathrm{rpm}$$? (Use $$I = \frac{1}{2}MR^2$ and $$\omega = 2\pi f$$)

Accepted Answer

$$t = 355\ \mathrm{s}$$

Question 8

Which of the following will NOT increase the torque you can exert on a stuck door?

Accepted Answer

Pushing closer to the hinge

Question 9

A car tire of radius $$0.30\ \mathrm{m} is $$rolling without slipping at $$29\ \mathrm{m/s}. $$What is the angular velocity $$\omega of $$the tire?

Accepted Answer

$$\omega = 96.7\ \mathrm{rad/s}$$

Question 10

A uniform seesaw balances when a 22 kg child sits 1.6 m from the pivot. Where should a 25 kg child sit to balance the seesaw?

Accepted Answer

1.41 m from the pivot, on the opposite side

Question 11

A force of $$240\ \mathrm{N} is $$applied at $$0.75\ \mathrm{m}$$ from a door hinge at $$20^\circ$$ from perpendicular. What is the torque?

Accepted Answer

$$	au = 169\ \mathrm{N\cdot m}$$

Question 12

A rigid body rotates about a fixed axis. Which statement is true?

Accepted Answer

All points have the same angular velocity

Question 13

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

Accepted Answer

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

Question 14

The moment of inertia of an object depends on:

Accepted Answer

Both the mass and how the mass is distributed relative to the axis

Question 15

A torque that tends to rotate an object in a clockwise direction is:

Accepted Answer

Negative

Question 16

A disk rotates with constant angular velocity $$\omega. $$What is the period $$T of $$rotation?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Question 17

A rolling wheel moves forward one circumference in one revolution. If the radius is $$r$$ and angular velocity is $$\omega$$, what is the velocity of the center?

Accepted Answer

$$v = r\omega$$

Question 18

A capstan is turned by a sailor pushing at a distance $$7R$$ from the axis, while the rope pulls at $$R$$ with tension $$T. $$What force $$F$$ must the sailor apply for zero net torque?

Accepted Answer

$$F = T/7$$

Rotational Motion: Physics with Calculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards