# Quick question about circular motion

1. Oct 22, 2008

### mjolnir80

what is the relation between the centripetal acceleration, angular acceleration and tangential acceleration in circular motion?
for example if the centripetal acceleration vector is getting larger for an object in circular motion does this mean something is also happening to the tangential acceleration and angular acceleration?

2. Oct 23, 2008

### Andrew Mason

It depends on what is happening to the radius of circular motion.

Centripetal acceleration = $v^2/R = 4\pi^2 R/T^2$

Angular acceleration = $\alpha = \dot \omega = d/dt(v/r) = 2\pi d/dt(1/T)$

Tangential acceleration = $\dot v = d/dt(2\pi R/T)$

AM

3. Oct 23, 2008

### mjolnir80

lets suppose the radius is constant but the centripetal acceleration vector is getting smaller
what would happen to the other 2 accelerations?

4. Oct 23, 2008

### Staff: Mentor

Since centripetal acceleration is given by vĀ²/r, that means that v is decreasing. Which means there will be a tangential and an angular acceleration.

5. Oct 23, 2008

### mjolnir80

so if the centripetal acceleration is constant then angular and tangential acceleration are zero?

thanks for the help!

6. Oct 23, 2008

### Staff: Mentor

Yes. If the radius is constant and the magnitude of the centripetal acceleration is constant, then the tangential speed is constant. And if the tangential speed is constant, the angular and tangential accelerations are zero.