Explain Circular and Orbital Motion

Let's start by looking at circular motion with constant speed. Can there be acceleration in this problem? Yes, velocity includes speed and direction and acceleration can mean speeding up, slowing down, or moving at constant speed but changing directions. During circular motion, the object in circular motion is constantly changing the direction of its motion.

Consider a yo-yo that you are swinging in a circle parallel to the ground, above your head. What keeps the yo-yo changing direction? The string does. If the string breaks, the yo-yo will no longer move in a circle. The tension in the string supplies the force to accelerate the yo-yo into circular motion.

If the length of the string is r (in meters), the speed is v (in m/s), the time to complete one revolution, one time around your head, is called the period, T(in seconds).

v = 2pr / T in the tangential direction

and ac = V₂ / r inward in radial direction

this is called the centripetal acceleration (in m/s²) and is supplied by a centripetal force (in newtons) of

Fc = mv²/r inward in radial direction

supplied by the string where m is the mass (in kg) of the yo-yo.