Circular Motion

In lesson 8, we discussed the analysis model of a particle in uniform circular motion, in which a particle moves with constant speed `v` in a circular path having a radius `r`. The particle experiences an acceleration that has a magnitude
`a_c = v^2/r`
The acceleration is called centripetal acceleration because `vec(a_c)` is directed toward the center of the circle. Furthermore, `vec(a_c)` is always perpendicular to `vec(v)`. Newton’s second law is applied along the radial direction, and the net force causing the centripetal acceleration can be related to the acceleration as follows:
`sum F = ma_c =m v^2/r`
A force causing a centripetal acceleration acts toward the center of the circular path and causes a change in the direction of the velocity vector. Above Figure shows if the string breaks at some instant, the puck moves along the straight-line path that is tangent to the circle at the position of the puck at this instant.