What happens in non-uniform circular motion?

[BomboshMan]

Hi,

Say there's a particle moving with just a radial component of acceleration, this will stay in circular motion because the acceleration is always perpendicular to the velocity. But if you introduce a tangential component of velocity, according to my book the particle stays in circular motion but it's tangential velocity changes. Why does this happen instead of the particle just moving in a path that isn't circular? Like an oval or something, seeing as the net acceleration no longer always points to the same place (centre of a circle).

Thanks

 

[mfb]

Say there's a particle moving with just a radial component of acceleration, this will stay in circular motion because the acceleration is always perpendicular to the velocity.

This is true for a very special value of acceleration only.
You don't have to get a circular motion.

 

[arildno]

1. IF the acceleration is always perpendicular to the velocity, and non-zero, THEN you have circular motion.
Basically, as mfb says you, have muddled it.

2. However: If you make the PREMISE that you have circular motion, then it follows that if the speed is constant, your acceleration is strictly radially directed, but if the speed is non-constant, then you have a non-zero, non-radial acceleration component.