Uniform Circular Motion
Motion in a circle at constant speed, with centripetal acceleration ac = v2/r directed towards the centre.
What is Uniform Circular Motion?
Motion in a circle at constant speed, with centripetal acceleration ac = v2/r directed towards the centre.
Key formula / rule: ac = v2/r = w2 r, always centre-directed.
Key points
- Derive the expression for centripetal acceleration.
- Compute period, speed and acceleration for circular motion data.
- Compare uniform circular motion with non-uniform circular motion.
Common exam trap
Claiming acceleration is zero because speed is constant.
Definitions
- Term
Uniform Circular Motion
- Meaning
Motion in a circle at constant speed, with centripetal acceleration ac = v2/r directed towards the centre.
- Term
Uniform Circular Motion — explanation
- Meaning
Constant speed does not mean constant velocity: direction changes continuously, so acceleration exists and points to the centre. Angular velocity w = v/r links the linear and angular descriptions.
Learning objectives
Derive the expression for centripetal acceleration.
Compute period, speed and acceleration for circular motion data.
Compare uniform circular motion with non-uniform circular motion.
Formulae
- Key point
ac = v2/r = w2 r, always centre-directed.
- Key point
Period T = 2 π r / v; frequency f = 1/T.
- Key point
Speed is constant, velocity is not.
Prerequisites
PHY-U1-KIN-T2-S1-C2
Common mistakes
Claiming acceleration is zero because speed is constant.
Inventing an outward 'centrifugal force' in an inertial frame.
Keywords
Uniform
Circular
Motion
Practice preview
Which of the following statements is true for Uniform Circular Motion (UCM)?…
easy
A particle of mass m is performing Uniform Circular Motion on a frictionless horizontal table with speed v, attached to a string passing through a hole in the centre of the table. If the string is slowly pulled down, red…
hard
A particle completes 10 revolutions in 5 seconds in a circular path of radius 2 m. What is its linear speed?…
medium