Classical Mechanics
Circular Motion Calculator
Calculate centripetal force, acceleration, angular velocity and orbital period from mass, velocity and radius.
Centripetal Force
Fc = mv²/r
Centripetal Acc.
—
m/s²
Angular Velocity (ω)
—
rad/s
Period (T)
—
s
Frequency (f)
—
Hz
Step-by-Step Solution
What is Circular Motion?
Circular motion occurs when an object moves along a circular path at constant speed. Although the speed is constant, the direction of velocity continuously changes — meaning the object is always accelerating toward the centre. This centripetal acceleration is caused by a centripetal force (gravity, tension, friction, etc.).
Fc = mv²/r
m = mass (kg) | v = velocity (m/s) | r = radius (m) | Fc = centripetal force (N)
💡 Centripetal means "centre-seeking". The force always points inward. There is no outward "centrifugal force" — that is a fictitious force felt in the rotating frame of reference.
Real-World Applications
Orbital Mechanics
Satellites orbit because gravity provides exactly the centripetal force needed to maintain circular motion.
Fairground Rides
The seat and harness provide centripetal force to keep passengers on the circular path.
Road Curves
Friction between tyres and road provides centripetal force. At high speeds, banking supplements friction.
Centrifuge
Spins at high ω to generate large centripetal acceleration, separating substances by density.
Frequently Asked Questions
What provides the centripetal force?
It depends on the system. For a satellite: gravity. For a ball on a string: tension. For a car on a curve: friction. For a banked road: the normal force component. Centripetal force is not a new type of force — it is whatever force keeps the object on a circular path.
What is the difference between centripetal and centrifugal force?
Centripetal force is real and points inward. Centrifugal force is a fictitious force that appears in a rotating reference frame — it seems to push you outward, but it is really your inertia resisting the change of direction.
What is angular velocity?
Angular velocity ω = v/r (rad/s) measures how fast the angle changes. One full revolution = 2π radians. Frequency f = ω/(2π) Hz. Period T = 1/f = 2π/ω seconds.