# Rotational mechanics

1. Dec 8, 2015

### vaibhav garg

1. A ball of mass m is placed in a smooth groove at the centre of disc and the frame starts to rotate with angular speed w, which if the following statement are incorrect?
1) Net force on the ball is towards center.
2) Motion of ball is in radially outward direction w.r.t center.
3) Centripetal force is mw^2r
4) Motion of ball is circular.
The answer to the given question states statements 1, 3 and 4 as incorrect.

2. centripetal force = mw^2r (towards center)

3. Shouldn't statement 2 be wrong as the centripetal force acts towards the center and statement 1 be correct.

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2. Dec 8, 2015

### PeroK

If answers 1 and 3 are correct, then what is the agent of the force directed towards the centre?

3. Dec 8, 2015

### vaibhav garg

I don't know but then again what agent would be there for it to move radially outwards.

4. Dec 8, 2015

### vaibhav garg

also 3 would be wrong anyway because if it moved the radius wold be varying.

5. Dec 8, 2015

4

6. Dec 8, 2015

### PeroK

That's quite a good question. If the ball started at the centre of the disc, then there is an argument that it would stay there. But, if it started slighty off-centre, then it can't move in a circle, because there is nothing to give it the necessary centripetal acceleration. It can't move back towards the centre, as that would also require acceleration towards the centre. So, by a process of elimination, it must move radially outwards.

Can you see why this radially outward motion is viable? What is pushing on the ball - and in what direction?

7. Dec 8, 2015

### vaibhav garg

The centrefugal force ?

8. Dec 8, 2015

### PeroK

The centrifugal force isn't a "what". Something physical must be forcing the ball out.

Note that the ball is not moving directly radially outwards from an external viewpoint: it's curving out in a spiral.

9. Dec 8, 2015

### vaibhav garg

I can't think of anything...

10. Dec 8, 2015

### PeroK

It has to be the groove.

11. Dec 8, 2015

### vaibhav garg

but wouldn't the grove be applying the normal force in just the perpendicular direction ?

12. Dec 8, 2015

### PeroK

Yep! Draw a diagram. The normal force (in the direction of $\hat{\theta}$) induces outward motion!

Consider this.

a) You have a ball on a string that's fixed to some centre point. You push the ball in the direction of $\hat{\theta}$, constantly changing the direction of your force to accelerate the ball in a circle. But, the string is necessary to hold the ball in.

b) Without the string, you push the ball, but in addition to accelerating in the $\hat{\theta}$ direction, it also moves away from the centre. That's because $\hat{\theta}$ and $\hat{r}$ are changing direction.

With respect to a fixed origin: An impulse in the $\hat{\theta}$ direction causes motion in that direction, but as the ball moves the direction of motion is no longer only in the $\hat{\theta}$ direction: increasingly, in fact, it becomes motion in the $\hat{r}$ direction.

Try it out!

13. Dec 8, 2015

### vaibhav garg

Now, I get it. Thanks