Centripetal Force Calculator

Centripetal force is the net inward force required to keep an object moving in a circular path. It always points toward the center of the circle. The word centripetal comes from Latin meaning 'seeking the center'. For a car turning a corner, this force is provided by friction between the tires and the road. For a satellite, it is provided by gravity. The magnitude is Fc = mv²/r, where m is mass, v is speed, and r is the radius of the circular path.

Centripetal force is a real force directed inward toward the center of circular motion. Centrifugal force is a fictitious or pseudo-force that appears to push outward in a rotating reference frame. In an inertial (non-rotating) reference frame, centrifugal force does not exist. The sensation of being pushed outward when a car turns is your body's inertia resisting the change in direction, not a real outward force. Physics problems are typically solved in inertial frames using only centripetal force.

Centripetal acceleration (ac) is the inward acceleration that changes the direction (but not speed) of circular motion. It equals v²/r or equivalently omega²*r. By Newton's second law, force equals mass times acceleration, so centripetal force Fc = m * ac = m * v²/r. Both centripetal force and centripetal acceleration point toward the center of the circle at every instant.

Centripetal force appears in many everyday situations: a car rounding a bend (friction provides the inward force), a ball on a string swung in a circle (string tension provides inward force), a planet orbiting the Sun (gravity provides inward force), a washing machine drum spinning clothes (the drum wall pushes clothes inward), and a roller-coaster loop (the track and gravity combine to provide inward force at the top). The formula Fc = mv²/r applies in all these cases.

Angular velocity (omega, symbol: rad/s) is the rate at which an object sweeps angle in a circle. Linear speed v and angular velocity omega are related by v = omega * r, where r is the radius. The period T = 2*pi/omega is the time for one full revolution. Frequency f = 1/T is the number of revolutions per second (Hz). At constant speed, increasing the radius of a circular path reduces the angular velocity even though linear speed stays the same.