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.
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Circular Motion Guide
What do I need to know about 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.
What's the key thing to understand about 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.
What should I know about 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.
What's the key thing to understand about 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.