Uniform Circular Motion
Lesson notes
Overview
Constant speed but changing direction means constant acceleration toward the centre. This topic is rated beginner and is number 14 of 227 in Physics. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows objects with force arrows, so you can see how the net force changes the motion. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
An object going round a circle at constant speed is still accelerating, because its velocity changes direction. The acceleration is directed toward the centre and has magnitude a = v²/r = ω²r. The speed stays constant but the velocity does not. The period T = 2πr/v is the time for one lap. This centripetal acceleration explains why a car taking a bend needs a sideways force.
Reading the relationship
The expression "a_c = v²/r = ω²r" is a compact summary of the idea. It uses the symbols a_c, v, r, ω; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, and a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.
Try this
Start by only moving one slider at a time. Say aloud what you expect, then check.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Terminal Velocity”, the topic before it in Physics. Once you are comfortable, continue with “Centripetal Force”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Uniform Circular Motion” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Uniform Circular Motion?
Constant speed but changing direction means constant acceleration toward the centre. It is a beginner topic in Physics.
How do I use the Uniform Circular Motion simulation?
The panel at the top shows objects with force arrows, so you can see how the net force changes the motion. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression a_c = v²/r = ω²r packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Terminal Velocity”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.