Uniform Circular Motion
From Section recall that when a body moves in a circle (or a circular arc) at constant speed v, it is said to be in uniform circular motion.
Rounding a curve in a car. You are sitting in the center of the rear seat of a car
moving at a constant high speed along a fiat road. When the driver suddenly turns left, rounding a comer in a circular are, you slide across the seat toward the right and then jam against the car wall for the rest of the turn. What is going on? While the car moves in the circular arc. it is in uniform circular motion.
Both you and the shuttle are in uniform circular motion and have accelerations directed toward the center of the circle. Again by Newton’s second law, centripetal forces must cause these accelerations. This time centripetal forces are gravitational pulls (the pull on you and the pull on hurtle) by Earth, radially inward, toward the center of Earth.
Another example of a centripetal force is shown in . There a hockey puck moves around in a circle at constant speed v while tied to a string looped
around a central peg. This time the centripetal force is the radially inward pull on the puck from the string. Without that force, the puck would slide off in a straight line instead of moving in a circle.
A centripetal force accelerates a body by changing the direction of the body’s velocity .without changing the body’s speed.
From Newton’s second law and ,we can write the magnitude F of a centripetal force (or a net centripetal force) as
However, the directions of the centripetal acceleration and force are not constant they vary continuously so as to always point toward the center of the circle. For this reason, the’ force and acceleration vectors are sometimes drawn along a radial axis r that moves with the body and always extends from the center of the circle to the body.