# Rotational Dynamics

1. Nov 16, 2013

### aerograce

When I am browsing through my rotational dynamics chapter, I raise myself a question on the direction of frictional force under all kinds of possible circumstances:

1. Pure rolling

For pure rolling, the frictional force will always be 0;

2. Non-pure rolling
For this situation, I will analyse with a model: A rolling ball lying on a level ground. And to simplify my listing, I will ignore some situations if they are similar to each other.

2.1 ω anti-clockwise v left

(1) ωR<v

Frictional force will tend to slow V down and increase ω, hence it is to the right;

(2) ωR>v

Frictional force will tend to increase V up and slow ω down. Hence it is to the left;

2.2 ω anti-clockwise v right

At first, the frictional force will be to the left(Slow down both ω and v)

But later, I think two situations may occur:

ω is not sufficiently large but v is sufficiently large, ω will be decreased to 0. And continuously, frictional force will be to the left to increase ω clockwisely until pure rolling occurs.

v is not sufficiently large but ω is sufficiently large, v will be decreased to 0. And after that, frictional force will be to the left to increase v leftwards until pure rolling occurs.

If ω and v just happen to be such nice that it will be decreased to 0 at the same time, the object will just stop then.

My idea in analyzing the frictional force is that: Non-pure rolling will always tend to transit itself into pure-rolling condition.

Thank you for spending time on reading this but could you please tell me whether my analysis is correct?

2. Nov 16, 2013

### CWatters

That seems consistent with what happens when you drive a car.