Uniform circular motion
What keeps it turning?
Swing a ball on a string in a circle at a steady speed.
Its speed stays the same, but its direction keeps changing.
A changing direction means a changing velocity, so there must be an acceleration.
That acceleration always points to the centre. We call it centripetal acceleration.
Explore it in 3D
- Drag to orbit the view. Scroll or pinch to zoom.
- Double the speed and watch the acceleration arrow grow four times.
- Press “Cut the string” and watch which way the ball flies.
Quick check
A ball is whirled in a horizontal circle. At the moment the string breaks, which way does the ball go?
- Straight towards the centre
- Straight away from the centre
- Along the tangent, the way it was moving
- It keeps moving around the circle
Answer
C. The string was the only thing pulling the ball towards the centre. Once it breaks there is no sideways force, so the ball keeps its velocity at that instant and flies off along the tangent.
Summary
- Speed and angular speed:
v = ωr - Centripetal acceleration:
a = v²/r = ω²r - Time for one round:
T = 2πr / v
- In uniform circular motion the speed is constant but the velocity is not, because its direction keeps changing.
- The acceleration always points towards the centre.
- Double the speed and the acceleration becomes four times bigger.