Nonuniform circular motion question

[alingy1]

I'm thinking about this: what happens if a nonuniform circular motion goes on for a long time?

centripetal acceleration=tangential speed^2/r.

If there is an existent tangential acceleration: tangential speed increases. So, centripetal acceleration must also increase. Therefore, after a very long time, the limiting case would be that the tangential acceleration becomes very small and the acceleration points towards the centre of the circle (if the string that sustains the bob (just an example) can support the acceleration)!

Does centripetal acceleration change overtime?

 

[Andrew Mason]

I'm thinking about this: what happens if a nonuniform circular motion goes on for a long time?

centripetal acceleration=tangential speed^2/r.

If there is an existent tangential acceleration: tangential speed increases. So, centripetal acceleration must also increase. Therefore, after a very long time, the limiting case would be that the tangential acceleration becomes very small and the acceleration points towards the centre of the circle (if the string that sustains the bob (just an example) can support the acceleration)!

Does centripetal acceleration change overtime?

For circular motion, the centripetal acceleration is always ω²r or v²/r . Tangential acceleration does not affect this, ever. This is because the tangent direction is always perpendicular to the radial direction.

AM

 

[alingy1]

@Andrew Mason: Since it is w^2r, w is increasing because of tangential acceleration, so centripetal acceleration is also increasing no?

 

[consciousness]

Yes it should increase.
If it doesn't, you get a spiral where the object gradually moves away from the center of the initial orbit.

 

[Andrew Mason]

@Andrew Mason: Since it is w^2r, w is increasing because of tangential acceleration, so centripetal acceleration is also increasing no?

It is the tangential speed and the radius, not the tangential acceleration, that determines the centripetal force for a body undergoing circular motion. Of course, a sustained tangential acceleration will affect tangential speed.

AM