Advanced · 13 min
Uniform circular motion
Find the inward acceleration and net force needed to follow a circular path.
Constant speed can mean acceleration
In uniform circular motion, speed stays constant but velocity changes direction continuously. The acceleration points towards the circle's centre and has magnitude a = v² ÷ r. This is called centripetal acceleration. Doubling speed at the same radius multiplies the required acceleration by four. At an instant, the velocity points along a tangent, perpendicular to the inward acceleration.
Worked example
An object moves at 6 m/s around a circle of radius 3 m. Inward acceleration = 6² ÷ 3 = 12 m/s²
Identify the inward force
The net inward force required is F = m × v² ÷ r. Centripetal force is a description of the net inward force, not an extra force to add to a diagram. Depending on the situation, tension, friction, gravity, or a combination supplies it. If no net force acts after an object leaves the circular path, it continues along the tangent at constant velocity.
Worked example
A 2 kg object travels at 3 m/s around a circle of radius 1.5 m. Required net inward force = 2 × 3² ÷ 1.5 = 12 N
Mark velocity and acceleration
- Draw an object at three points around a circular path. At each point, draw a tangent velocity arrow and an inward acceleration arrow.
- At a fixed radius, compare the required inward force at 5 m/s and 10 m/s for the same mass.