Quick question about circular motion

[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?

 

[Andrew Mason]

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?

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

 

[mjolnir80]

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

 

[Doc Al]

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

Since centripetal acceleration is given by v²/r, that means that v is decreasing. Which means there will be a tangential and an angular acceleration.

 

[mjolnir80]

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

thanks for the help!

 

[Doc Al]

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

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.