# Rolling and friction

1. Jul 21, 2014

### jaumzaum

I want to describe the motion of a ball that rolls without slipping in a plane where acts a force field not in the direction of the motion. To illustrate better, the ball is put on the origin, there is a field h in y direction, and a velocity v0 in the x direction. There is also a friction force parallel to the plane in a way that the balls always rolls without slipping in the plane. How can I calculate y in function of x?

http://imagizer.imageshack.us/v2/280x200q90/673/08e7ea.png [Broken]

I've tried to solve this, but I'm having problems. I know the only torque acting on the particle is Ff.R (Ff = friction force, R is the radius of the ball). So Ff.R = I.γ (I is inertial momment of the ball, γ is the angular acceleration). If I substitute I by 2/5 MR² and γ by a/R I get Ff = 2/5 Ma. But the problem is there, can I do this substitution? Also, is the direction of the friction force opposite to the instantaneous velocity of the particle? Is the ball is rolling in a way that $\vec{ω}$ is always perpendicular to $\vec{v}$? I don't know how to go on from there.

Last edited by a moderator: May 6, 2017
2. Jul 21, 2014

### rcgldr

For the side force, you could imagine that the ball is rolling initially horizontally on an inclined plane, with force perpendicular to the initial velocity = m g sin(θ), where θ is the angle of the plane (from a level planel). The force is only initially perpendicular to the path; as soon as the ball starts to roll downwards on the inclined plane, a component of the force is in the same direction as the path of the ball.

Complicating matters is the fact that the ball's axis of rotation is yawing (relative to the plane), and I'm not sure if some type of gyroscopic precession effect would be involved and/or if a twisting torque occurs at the point of contact (assuming zero slippage).

Last edited: Jul 21, 2014
3. Jul 22, 2014

### Delta²

What sort of force field is h? Is it the gravitational field? if it isnt the gravitational field what is the formula for the force exerted by the h field to the ball? Do we also assume there is gravitational field in this problem (perpendicular to the x-y plane of the given figure)?

4. Jul 22, 2014

### Delta²

Well anyway seems to me that the condition imposed of "rolling without sliding" means that the velocity of the c.o.m is always equal and opposite of the linear velocity of the point of contact , hence the friction force is also in the opposite direction of the c.o.m velocity.

5. Jul 22, 2014

### jaumzaum

Sorry I forgot to say
There is a gravitacional field perpendicular to the Sheet, otherwise there would be no friction

Force exerced on ball is m h

6. May 15, 2015

### Muhammed Arif

See my article " The polygon model of rolling friction" in the journal IJEERT

7. May 15, 2015

### Tom_K

8. May 22, 2015

### theodoros.mihos

This is not so simple. Rolling balls have angular momentum that change in direction by external forces:
$$\textbf{τ} = \frac{\partial\mathbf{L}}{\partial{t}}$$