Circular Motion Calculator

Circular motion occurs whenever an object follows a curved path around a center. Even when its speed stays constant, its velocity changes because velocity includes direction. That continuous directional change requires an inward acceleration called centripetal acceleration. Its magnitude is a = v² ÷ r, where v is tangential velocity and r is the radius of the path. The acceleration always points toward the center rather than along the direction of travel. Newton's second law connects that acceleration to centripetal force. Multiplying by mass gives F = m × v² ÷ r. This is not a separate type of physical interaction; it is the name for the net inward force supplied by tension, gravity, friction, a normal force, or another real interaction. A string supplies it for a spinning ball, tire friction supplies it for a turning car, and gravity supplies it for an orbiting satellite. The equations reveal useful trends. Doubling mass doubles the force needed at the same speed and radius. Doubling speed quadruples both acceleration and force because velocity is squared. Increasing radius reduces the required acceleration and force, so a wider turn is gentler at a fixed speed. Rearranging the force equation gives v = square root of F × r ÷ m and r = m × v² ÷ F, enabling this calculator to solve several common unknowns. These relationships help compare everyday turns, rotating machinery, laboratory demonstrations, and idealized orbital motion. All inputs here use SI units: kilograms, meters, seconds, and newtons. Convert kilometers per hour to meters per second by dividing by 3.6 before entering a speed. Use the distance from the rotation axis to the object's center of mass as radius. The calculation assumes uniform speed and a circular path. It does not model changing speed, bank angles, aerodynamic effects, structural deformation, or safety limits. Engineering and amusement-ride decisions should include dynamic loads and appropriate safety factors beyond this idealized result.