Moment of Inertia and Angular Momentum
Rotational inertia and angular momentum are the spinning analogues of mass and momentum.
About this topic
Moment of inertia I measures resistance to changes in rotation and depends on how mass is spread out: I = Σmr². Mass further from the axis counts more. Angular momentum is L = Iω, and torque equals the rate of change of L. These are the rotating equivalents of mass, momentum and force.
In the absence of external torque, angular momentum is conserved. A spinning ice skater pulls her arms in, so I decreases and ω increases to keep L constant, making her spin much faster. A diver tucks to spin quickly and then extends to slow down for entry. Cats use the same idea to twist and land on their feet.
Worked example: a skater with I = 3.0 kg·m² spinning at 2 rev/s pulls her arms in and drops to I = 1.0 kg·m². Conservation gives ω = 3 × 2 / 1 = 6 rev/s. Shapes matter: a solid disc has I = ½MR², a hoop MR², so a hoop rolls down a ramp more slowly than a solid disc of equal mass.
Gyroscopes and spinning wheels resist tipping because of angular momentum, which is used in navigation and to stabilise spacecraft and bicycles. Planets also keep their spin for the same reason. Students often think I is a fixed property of an object; it depends on which axis you spin it around.
Key ideas
- L = Iω
- Skaters spin faster pulling arms in
- Angular momentum is conserved
Quick check
Use cases: where Moment of Inertia and Angular Momentum helps
- Homework: review the key idea behind Moment of Inertia and Angular Momentum before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Moment of Inertia and Angular Momentum without notes.
- Visual learning: play with the interactive lab to see how Moment of Inertia and Angular Momentum changes when you adjust its inputs.
- Teaching a friend: explain Moment of Inertia and Angular Momentum in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Moment of Inertia and Angular Momentum?
Rotational inertia and angular momentum are the spinning analogues of mass and momentum.
What will I learn in Moment of Inertia and Angular Momentum?
L = Iω. Skaters spin faster pulling arms in. Angular momentum is conserved.
Is Moment of Inertia and Angular Momentum part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Moment of Inertia and Angular Momentum lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Moment of Inertia and Angular Momentum?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.