Circular Motion & Centripetal Force Calculator
Calculate centripetal force, acceleration, angular velocity, and orbital period for objects in circular motion. Covers horizontal circles, banking, and satellite orbits.
Circular Motion Guide
Centripetal Force and Acceleration
For circular motion, a centripetal force acts toward the centre. F = mv2/r = m(omega)2r. Centripetal acceleration: a = v2/r. Centripetal force is not a new type of force — it is provided by an existing force. String tension for a ball on a string. Gravity for a satellite or moon. Friction for a car turning a corner. Normal reaction on a banking road. Example: 2kg ball on 5m string at 10 m/s. F = 2 x 100/5 = 40N inward.
Angular Velocity and Period
Angular velocity omega = 2pi/T = 2pif. Linear speed v = omega x r. Period T = 2pir/v. Earth rotation: T = 86400s. omega = 2pi/86400 = 7.27 x 10 to the -5 rad/s. Speed at equator (r = 6.37 x 10 to the 6 m): v = 463 m/s.
Vertical Circles and Minimum Speed
At the top of a vertical circle: T + mg = mv2/r. Minimum speed for string to remain taut (T=0): v_min = sqrt(gr). Below this speed the string goes slack. At the bottom: T = mv2/r + mg. Tension is always greatest at the bottom of the circle. Applications: roller coaster loops, bucket of water demonstration.
Satellites and Orbits
Gravity provides centripetal force: GMm/r2 = mv2/r. Orbital speed v = sqrt(GM/r). Period T = 2pi x sqrt(r3/GM). Geostationary orbit: T = 86400s, altitude 35786km above Earth. Low Earth orbit (ISS at 400km): T approx 92 minutes. Kepler third law: T2 is proportional to r3 follows directly from these equations.
Recommended for this calculator