Centripetal Force: Understanding the Basics

[a.mlw.walker]

Hi, I am having trouble grasping an idea.

If you have a ball taped to a bit of string, and spin it above your head the ball will stay the radius away from your hand. If you spin faster and faster the "lack of centreptal force" - the centrefugal force will be greater than the force gluing the ball to the string and you reach the escape velocity?

What happens if the ball is held on a track and spinning so it can't move outwards because of a metal track but if it stopped it would fall inwards - like a ball on a roulette wheel. Surely the value of centrepetal force is not the reason it falls inwards in this example, because it is relative to the ball. There must be another force that the centreptal force of the ball must be greater than to keep it on the track (or in the example with ball on string, the centrepetal force must be greater than another force?)

What is this force - is it gravity F=mg. For both scenarios

If centreptal force falls below F = mg value, then ball will fall from the track?

Thanks

Alex

 

[Doc Al]

I'm not sure I can pinpoint your exact question, but I'll give it a shot.

If you have a ball taped to a bit of string, and spin it above your head the ball will stay the radius away from your hand. If you spin faster and faster the "lack of centreptal force" - the centrefugal force will be greater than the force gluing the ball to the string and you reach the escape velocity?

Whenever something moves in a circle, there must be a centripetal force providing the centripetal acceleration. (Without a centripetal force pulling it in, the object would just keep going in a straight line.) The faster that something moves, the greater the acceleration required and thus the greater the force required. In the case of your ball and string, if the centripetal force required is too much (you have it going too fast) the tape will rip off (or the string will break) and the ball will shoot off in a straight line (of course, other forces act on the ball also--such as gravity).

What happens if the ball is held on a track and spinning so it can't move outwards because of a metal track but if it stopped it would fall inwards - like a ball on a roulette wheel. Surely the value of centrepetal force is not the reason it falls inwards in this example, because it is relative to the ball. There must be another force that the centreptal force of the ball must be greater than to keep it on the track (or in the example with ball on string, the centrepetal force must be greater than another force?)

Again, since the ball is moving fast it "wants" to just go straight (Newton's 1st law) but the contact force of the metal track exerts an inward force that keeps it moving in a circle.

It may be helpful to view things from the accelerating frame of the roulette wheel. In that frame there is a non-inertial outward force (called the centrifugal force) pushing the ball against the track, as well as gravity acting to pull it down. When the wheel slows down, the centrifugal force reduces. Eventually gravity overcomes that outward force and the ball begins to roll down the incline.

If I missed your question, please rephrase it.

 

[a.mlw.walker]

No thanks you answered it. I wanted to know whether it was gravity that the centrefugal force had to be reater than to keep the ball on the track - or inside edge of the rouletter wheel. As the ball slows, the force of gravity is greater than the centrafugal force, and the ball will fall right...