Q: The angular displacement $$\Delta\theta of a $$rotating rigid body is given by which of the following equations for constant angular acceleration?

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

Question 1

A wind turbine blade rotates with a constant angular acceleration. If it starts from rest and reaches an angular velocity of $$10\ \mathrm{rad/s} in$$ $$5\ \mathrm{s}$$, what is its angular acceleration?

Accepted Answer

$$0.5\ \mathrm{$$rad/s^2$$}$$

Question 2

A compact disc spins up from rest to $$7200\ \mathrm{rev/min} in$$ $$4.0\ \mathrm{s}. $$What is its average angular acceleration in $$\mathrm{$$rad/s^2$$}$$?

Accepted Answer

$$30\pi\ \mathrm{$$rad/s^2$$}$$

Question 3

A merry-go-round rotates at a constant rate. A boy is at the edge and a girl is near the center. How do their angular velocities compare?

Accepted Answer

Both children have the same angular velocity.

Question 4

A rotating fan blade is slowing down in the counterclockwise direction. What are the signs of $$\omega ($$angular velocity) and $$\alpha ($$angular acceleration)?

Accepted Answer

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

Question 5

A tractor wheel rotates through an angle of $$25\ \mathrm{rad} in $$time $$t$$ from rest with constant angular acceleration. Through what angle will it have turned after time $$2t$$?

Accepted Answer

$$100\ \mathrm{rad}$$

Question 6

A gyroscope spins up from rest to $$25\ \mathrm{rpm} in $$time $$t$$ with constant angular acceleration. What will its angular velocity be after time $$2t$$?

Accepted Answer

$$50\ \mathrm{rpm}$$

Question 7

The angular displacement $$\Delta	heta of a $$rotating rigid body is given by which of the following equations for constant angular acceleration?

Accepted Answer

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

Question 8

A child pushes a merry-go-round, causing it to accelerate from rest. If the angular acceleration is $$2\ \mathrm{$$rad/s^2$$}$$, what is the angular velocity after $$3\ \mathrm{s}$$?

Accepted Answer

$$6\ \mathrm{rad/s}$$

Question 9

A rotating disk has an angular velocity of $$5\ \mathrm{rad/s}$$ and an angular acceleration of $$-1\ \mathrm{$$rad/s^2$$}. $$How long will it take to come to rest?

Accepted Answer

$$5\ \mathrm{s}$$

Question 10

A wind turbine blade sweeps out an arc of $$10\ \mathrm{m}$$ with a radius of $$5\ \mathrm{m}. $$What is the angular displacement in radians?

Accepted Answer

$$2\ \mathrm{rad}$$

Question 11

A rotating wheel increases its angular velocity from $$10\ \mathrm{rad/s} to$$ $$30\ \mathrm{rad/s} in$$ $$4\ \mathrm{s}. $$What is its average angular acceleration?

Accepted Answer

$$5\ \mathrm{$$rad/s^2$$}$$

Question 12

If a rigid body rotates $$3$$ full revolutions, what is the angular displacement in radians?

Accepted Answer

$$6\pi$$

Question 13

A machine part rotates at $$1200\ \mathrm{rpm}. $$What is its angular velocity in $$\mathrm{rad/s}$$?

Accepted Answer

$$40\pi\ \mathrm{rad/s}$$

Question 14

A rotating disk slows down with a constant angular acceleration. If its initial angular velocity is $$8\ \mathrm{rad/s}$$ and it comes to rest in $$4\ \mathrm{s}$$, what is the angular displacement during this time?

Accepted Answer

$$16\ \mathrm{rad}$$

Question 15

A wheel rotates with an angular velocity $$\omega = 10\ \mathrm{rad/s}$$ and an angular acceleration $$\alpha = 2\ \mathrm{$$rad/s^2$$}. $$What is its angular velocity after $$3\ \mathrm{s}$$?

Accepted Answer

$$16\ \mathrm{rad/s}$$

Question 16

A merry-go-round rotates counterclockwise. If $$\Delta	heta \u003e 0$$, what can you say about the sign of $$\omega$$?

Accepted Answer

$$\omega \u003e 0$$

Rotational Motion: Concepts, Equations, and Applications

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