Uniform circular motion

Also called UCM

Motion around a circular path at constant speed. The speed never changes but the velocity does, because its direction turns continuously, so the object accelerates toward the center of the circle at every instant.

Constant speed, changing velocity. That is the whole content of uniform circular motion: the speed holds still while the direction of travel turns every instant, and velocity is a vector, so the object accelerates all the way around.

The acceleration points at the center. Tangential acceleration is the rate at which speed changes, and here the speed does not change, so there is none. The net acceleration is purely centripetal and stays perpendicular to the velocity, which is exactly why the speed can hold while the direction does not.

Period TT is the time to complete one full circular path and frequency ff is the rate at which revolutions are completed, with T=1/fT = 1/f. One lap covers a circumference at constant speed, so T=2πr/vT = 2\pi r / v.

There is no outward force. In an inertial frame only the real inward forces exist; the outward shove a passenger feels on a bend is their own inertia carrying them straight on while the car turns underneath them.

Which real force supplies the inward pull, and how to set up loops, banked curves and conical pendulums, belongs to the centripetal force guide. Two boundary statements are worth knowing: AP Physics 1 only expects students to quantitatively analyze banked curves in which no friction is required to maintain uniform circular motion, and it does not expect students to know Kepler's first or second laws of planetary motion.

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