Ye Olde Acceleration: Angular Speed, Deceleration, & More

[a.mlw.walker]

hi,

if a motor spins a ball on a string round and round and a constant speed, there is an acceleration towards the centre, but no angular acceleration, just angular speed right?

but if you now turn the motor off, the balls angular acceleration will now go negative, and the ball will decelerate. at what point does the ball fall. how do you calculate how long it will take and at what speed the ball will fall at? because this is separate from its centrepetal acc yes?

 

[tiny-tim]

Hi a.mlw.walker!

if a motor spins a ball on a string round and round and a constant speed, there is an acceleration towards the centre, but no angular acceleration, just angular speed right?

Yes!

but if you now turn the motor off, the balls angular acceleration will now go negative, and the ball will decelerate. at what point does the ball fall. how do you calculate how long it will take and at what speed the ball will fall at? because this is separate from its centrepetal acc yes?

Friction will gradually reduce the speed of the ball, and therefore its angular velocity (as you say, the angular acceleration will now go negative), and this will start immediately.

What is supporting the ball (apart from the string)? If nothing is, then the ball will immediately start to go lower (on the surface of an imaginary sphere). But it won't actually "fall".

 

[Danger]

If this were to be done in space, though, with no air and microgravity, the effect would be different. In that case, stopping the motor would just cause the tether line to wind up around the shaft and draw the ball in until it hit centre. Then, depending upon the properties of the ball, it would possibly rebound and unwind just to wind up again in the opposite direction. Eventually, the losses due to collision with the centre would overcome the ability to unwind again.
At least, I think that's how it would go.

 

[a.mlw.walker]

well, yeah ok fine i didnt mention it for the example but if you want, the shaft has an arm on it and the string is attached to that so it can't "wind up"...

are you sure that effect is happening immediately, because with centrepetal force f=mv*v)/r

when this force gets below the force gravity has on the ball then the ball will begin to spiral down - but its only spiraling down because of a forward momentum, until the point where centreptal force is lower than the gravitational force, it will continue to spin on the same radius.

my question is how to work out how long after you turn the motor off, to when centreptal force is lower than gravitational force... it must be to do with the angular accelration but can't work out how to do it...

 

[tiny-tim]

… are you sure that effect is happening immediately, because with centrepetal force f=mv²)/r ...

Hi a.mlw.walker!

(copy the ², and anything else you want, for future use)

This is exactly the same as a ball rolling round the inside of a hemisphere.

Its height depends precisely on its speed.

Reduce the speed slightly, and that must reduce the height slightly … it does happen immediately.

So … on a sphere … what do you think is the formula connecting the speed with the height?