Key Concepts: Circular Motion & Centripetal Force

Uniform Circular Motion

• An object moving in a circle at constant speed is always accelerating because its direction changes.
• The acceleration points toward the center of the circle — called centripetal acceleration.
• a_c = v²/r, where v is speed and r is radius.

Centripetal Force

• The net inward force causing circular motion: F_c = mv²/r = mω²r.
• Centripetal force is not a new type of force — it's provided by existing forces (tension, gravity, friction, normal force).

Examples

• A car turning on a road: friction provides centripetal force.
• A ball on a string: tension provides centripetal force.
• The Moon orbiting Earth: gravity provides centripetal force.

Period and Frequency: T = 2πr/v, f = 1/T, ω = 2πf.