Circular Motion

Investigate how radius, mass and speed affect circular motion, centripetal acceleration and force.

Circular Motion Simulation

● Tangential velocity ● Centripetal acceleration ● Radius

Velocity is tangent to the circular path. Centripetal acceleration always points towards the centre.

Input Variables

0.5 m 10 m
0.5 m/s 20 m/s
0.1 kg 10 kg

Calculated Results

Centripetal acceleration
12.00 m/s²
Directed towards the centre
Centripetal force
24.00 N
Net inward force required
Angular velocity
2.00 rad/s
Period
3.14 s
Frequency
0.318 Hz

Circular Motion Equations

Centripetal acceleration
ac = v² / r

Acceleration required to change the direction of velocity.

Centripetal force
Fc = mv² / r

The net inward force responsible for the circular motion.

Angular velocity
ω = v / r

Angular displacement per second, measured in radians per second.

Period and frequency
T = 2πr / v
f = 1 / T

Period is the time for one revolution. Frequency is revolutions per second.

Understanding Circular Motion

An object moving in a circular path has a changing velocity because its direction continually changes, even if its speed remains constant.

  • Velocity: Acts tangent to the circular path.
  • Centripetal acceleration: Always points towards the centre of the circle.
  • Centripetal force: The net inward force that produces the centripetal acceleration.
  • Radius: Increasing the radius at constant speed reduces centripetal acceleration.
  • Speed: Increasing speed increases centripetal acceleration with the square of speed.

This simulation assumes uniform circular motion: the object's speed is constant and its path radius does not change. The force arrow represents the net inward force, not a separate type of force.