Angular Velocity
Angular velocity measures how fast an angle changes.
About this topic
Angular velocity ω measures how fast an angle changes, in radians per second: ω = Δθ/Δt = 2π/T = 2πf. All points on a rotating disc share the same ω, but points further out travel faster in a straight-line sense, with v = ωr. It matters because it lets us describe anything that spins, from wheels and fans to planets and hard drives, with a single number.
Its direction is given by the right-hand rule: curl the fingers of your right hand the way the object turns and your thumb points along the ω vector, along the axis of rotation. Radians are used because they make the link between arc length and angle simple: s = rθ. One full turn is 2π radians, or 360 degrees, so 1 revolution per second equals about 6.28 rad/s.
Worked example: a bicycle wheel of radius 0.35 m turns at 5 revolutions per second. Then ω = 2π × 5 ≈ 31 rad/s, and a point on the tyre moves at v = ωr ≈ 31 × 0.35 ≈ 11 m/s, about 39 km/h. A point halfway to the hub has the same ω but only half the speed.
Applications include motors, turbines, gyroscopes and the spin of the Earth, which turns at about 7.3 × 10⁻⁵ rad/s. A common mistake is to forget to convert rpm or degrees into rad/s before using formulas. Another is to think the inner and outer parts of a wheel turn at different rates; they share ω but differ in linear speed.
Key ideas
- ω = Δθ/Δt in rad/s
- v = ωr
- Period T = 2π/ω
Quick check
Use cases: where Angular Velocity helps
- Homework: review the key idea behind Angular Velocity before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Angular Velocity without notes.
- Visual learning: play with the interactive lab to see how Angular Velocity changes when you adjust its inputs.
- Teaching a friend: explain Angular Velocity 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 Angular Velocity?
Angular velocity measures how fast an angle changes.
What will I learn in Angular Velocity?
ω = Δθ/Δt in rad/s. v = ωr. Period T = 2π/ω.
Is Angular Velocity 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 Angular Velocity 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 Angular Velocity?
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.