Practice Angular Momentum 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 rotational equivalent of linear momentum, measuring the quantity of rotational motion in a spinning or orbiting object.

A spinning skater pulling their arms in spins faster — they're conserving angular momentum.

Showing a random 20 of 50 problems.

Example 1

medium

A merry-go-round (

I = 100\,\text{kg}\cdot \text{m}^2

) spins at

1\,\text{rad/s}

. A child adds

I = 25\,\text{kg}\cdot \text{m}^2

by stepping on at the rim. Find the new angular speed.

Example 2

easy

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

and

L = 20\,\text{kg}\cdot \text{m}^2/\text{s}

, find

I

Example 3

easy

A skater has

I = 2\,\text{kg}\cdot \text{m}^2

spinning at

4\,\text{rad/s}

. Find their angular momentum.

Example 4

easy

A solid disk has

I = \tfrac12 M R^2

. For

M = 4\,\text{kg}

R = 0.5\,\text{m}

\omega = 8\,\text{rad/s}

, find

L

Example 5

hard

A rod of length

L = 1\,\text{m}

, mass

M = 2\,\text{kg}

, pivots at its center. A

0.1\,\text{kg}

clay ball at

10\,\text{m/s}

hits the rod's end and sticks. Find the angular speed after. (

I_{rod,center} = \tfrac{1}{12}M L^2

Example 6

easy

A planet's angular momentum about the Sun is approximately conserved. True or false?

Example 7

hard

Show that if KE is conserved when a skater pulls in their arms (

I

halves), then

L

cannot be conserved. (Reach a contradiction.)

Example 8

medium

A solid disk (

M = 6\,\text{kg}

R = 0.4\,\text{m}

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

) is suddenly joined by a coaxial

4\,\text{kg}

disk of the same radius initially at rest. Find the new

\omega

Example 9

medium

A planet at perihelion moves at

60\,\text{km/s}

r = 1

unit; at aphelion

r = 4

units. Find its aphelion speed (conserve

L = mvr

Example 10

hard

3\,\text{m}

uniform rod (

M = 4\,\text{kg}

) lies on frictionless ice. A

0.2\,\text{kg}

puck moving at

8\,\text{m/s}

strikes it perpendicularly

1\,\text{m}

from the center and sticks. Find the angular speed of the rod+puck about their new center of mass. (

I_{rod,CM} = \tfrac{1}{12}M L^2

Example 11

medium

A merry-go-round of

I = 200\,\text{kg}\cdot \text{m}^2

is at rest. A

50\,\text{kg}

child runs tangentially at

3\,\text{m/s}

and jumps on at radius

2\,\text{m}

. Find the new angular speed.

Example 12

medium

A 4 kg point mass moves at

3\,\text{m/s}

along a line passing

2\,\text{m}

from a reference point (perpendicular distance). Find its angular momentum about that point.

L = mvd: velocity × perpendicular moment arm

Example 13

challenge

A figure skater spins at

1.0\,\text{rev/s}

with arms out (

I = 5\,\text{kg}\cdot \text{m}^2

). She tucks to

I = 1\,\text{kg}\cdot \text{m}^2

. Find her new rotational KE and the work she did.

Example 14

easy

A hoop of mass

2\,\text{kg}

and radius

0.5\,\text{m}

rolls so its center moves at

\omega = 10\,\text{rad/s}

. Find

L_{spin}

. (

I_{hoop} = MR^2

Example 15

easy

A spinning skater pulls in their arms, reducing

I

. What happens to their spin rate

\omega

(no external torque)?

Example 16

easy

What is the SI unit of angular momentum?

Example 17

challenge

A solid sphere (

I = \tfrac25 M R^2

M = 2\,\text{kg}

R = 0.1\,\text{m}

) rolls without slipping at

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

. Find its total angular momentum about a point on the ground directly below its current center.

Example 18

medium

A particle moves at constant velocity along a straight line that does NOT pass through point

O

. Is its angular momentum about

O

constant?

Example 19

easy

A wheel has

I = 5\,\text{kg}\cdot \text{m}^2

and spins at

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

. Find

L

Example 20

easy

Is angular momentum a vector or a scalar?

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Related Concepts

Torque Momentum