Practice Angular Velocity in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The rate at which an object rotates about an axis, measured in radians per second, with a direction along the axis.

How fast something is spinning — a car wheel spinning fast has high angular velocity.

Showing a random 20 of 50 problems.

Example 1

easy

What direction does the angular velocity vector point for a spinning wheel (right-hand rule)?

Example 2

medium

A car wheel of radius

0.30\,\text{m}

rolls without slipping at

v = 18\,\text{m/s}

. Find its angular velocity.

Example 3

medium

A bike speedometer reads

36\,\text{km/h}

with wheel radius

0.35\,\text{m}

. Find the wheel's

\omega

Example 4

medium

A clock's minute hand goes around once per hour. Find

\omega

in rad/s.

Example 5

medium

A wheel of radius

0.4

m rolls so its center moves at

8

m/s. Find the wheel's angular velocity.

Example 6

medium

A wheel starts at rest and reaches

\omega = 24\,\text{rad/s}

after

6\,\text{s}

at constant

\alpha

. Through how many radians did it turn?

Example 7

medium

A point at

r = 0.5\,\text{m}

moves with centripetal acceleration

a_c = 18\,\text{m/s}^2

. Find

\omega

Example 8

challenge

A wheel of radius

0.5

m starts at rest and reaches

\omega=12

rad/s in

4

s. Find the linear speed of the rim at

t=4

s and the rim's tangential acceleration.

Example 9

challenge

A car drives at

v = 25\,\text{m/s}

. Its tires have radius

0.32\,\text{m}

. How many full rotations does each tire make over a

5\,\text{km}

trip?

Example 10

easy

Convert

90°

to radians.

Example 11

challenge

Two gears mesh: gear A (radius

4

cm) drives gear B (radius

2

cm). If A spins at

\omega_A=6

rad/s, find

\omega_B

Example 12

easy

A turntable spins at

\omega = 5\,\text{rad/s}

. Find the linear speed of a point at

r = 0.15\,\text{m}

Example 13

challenge

A satellite in low Earth orbit has period

T = 90\,\text{min}

. Find its angular velocity in rad/s.

Example 14

hard

A cyclist accelerates from rest to

v = 12\,\text{m/s}

8\,\text{s}

. Wheel radius is

0.30\,\text{m}

. Find the wheel's angular acceleration.

Example 15

hard

On a record at

\omega = 4\pi\,\text{rad/s}

, point

A

is at

r = 0.05\,\text{m}

and point

B

is at

r = 0.15\,\text{m}

. How do their angular velocities and linear speeds compare?

Example 16

hard

A point on a

0.5\,\text{m}

radius disk has linear speed

v = 3\,\text{m/s}

. How many revolutions does the disk complete in

20\,\text{s}

at this rate?

Example 17

medium

A clock's second hand makes one revolution per minute. Find its angular velocity in rad/s.

Example 18

medium

A motor speeds from rest to

\omega=18

rad/s in

6

s. Find the angular acceleration.

Example 19

hard

A rotor's angular velocity follows

\omega(t) = 4 + 3t^2\,\text{rad/s}

. Find

\alpha

t = 2\,\text{s}

Example 20

easy

A turntable completes one revolution in

2

s. Find its angular velocity.

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Related Concepts

Circular Motion Velocity Angular Momentum