# Calculating minimum velocity around a loop

1. Oct 2, 2015

### Nouo

So I had this question for physics about something going around a loop. The question asked what the minimum velocity to counteract gravity is if something is going around a loop. hint: One force will be zero.

I'm not sure how to figure this out, can someone help?

2. Oct 2, 2015

### Mentallic

Can you calculate the centripetal acceleration of a particle moving at some velocity around the loop? You can assume the loop is of radius r and treat it as a constant.

3. Oct 3, 2015

### HallsofIvy

If an object is going around a loop of radius R at constant angular velocity, $\omega$ then its position vector (taking center of the loop to be (0, 0) and the objects position at t= 0 to be (1, 0)) is $R cos(\omega t)\vec{i}+ R sin(\omega t)\vec{j}$. Its velocity vector will be $-\omega R sin(\omega t)\vec{i}+ \omega R cos(\omega t)\vec{j}$ and its acceleration vector will be $-\omega^2 R cos(\omega t)\vec{i}- \omega^2 R sin(\omega t)\vec{j}$. In order to stay on the loop, the acceleration at the top ($\theta= \pi/4$) must be non-negative.