# Rotation caused by friction on a sphere

1. Oct 11, 2008

### cognaq

[I am new to this forum and I am sorry if posted this in the wrong topic.]

I just wondered if you could help me with the following (I know it's long :-( ):

I had the idea of calculating g (gravitational force) on Earth using a marble (spherical) and a slant board (a hard board that is tilted; theoretically a plane at some angle alpha to the horizontal). I would measure the time for the marble to go down the plane and the distance it goes down and then calculate the acceleration and get g from there.
Now there is a problem, namely, friction. It is easy to calculate the acceleration if there is no friction, but this is impossible for a practical experiment. Now, a marble that has some friction rolls down the plane (rotating obviously), while a marble without friction glides it down without any rotation at all (it could be a cube and it would give the same result).

I've done a simulation on my computer and it turned out - as I expected - that the marbles that had no friction were faster than the ones with friction. What is interesting, all the marbles I gave a friction coefficient from 0.02 to up to more than 2 rolled down with the same speed; the speed varied only when µ was between 0.000 and ~0.02. I found out that the marbles with such low coefficient of friction were not fully rolling, they were gliding and rolling.

Assuming that the friction of the plane and the marble is big enough to make the marble roll fully (not glide at all), how can I take this rotation caused by the friction into account, when wanting to measure the acceleration to find g? Is it the rotation that slows down the marbles? Or is it only the friction? Why are the differences in speed of marbles with and without friction so big, when the contact area of a sphere is so small? How can I include this in my calculations.

Thank you for reading it (it turned out to be even longer than I thought it would get). I hope you can help me.

2. Oct 11, 2008

### Rake-MC

Hmm that's an interesting one, and I have to admit that I'm not an expert in this at all.

My opinion is that it's solely the friction that slows down the marbles. The rotation does not play a part in slowing it down, rather the rotation is caused by more friction. Rotation would seem to me to be slower because more of the marble is in contact with the plane for more time, ie. it's not bouncing.

However, this could also play an opposite part by saying that not should be faster because there is not enough friction to make it rotate.. Gah!

Why are the differences so big, when the contact area is so small? Well that just depends on how you define big. I'm sure if you ran a ball the same size made of sand paper down a dirt hill it would be even bigger. So it's not necessarily so big, but so normal.

How can you include this into your calculations? Other than calculated forces * coefficient of kinetic friction, you'd have to ask someone else. Hope I gave some input.

3. Oct 11, 2008

### arildno

First off:
Friction does NOT dissipate any energy from a strictly rolling ball on a rigid plane at all, it merely converts a fairly large chunk of "linear" kinetic energy into rotational kinetic energy.

Since it is the actual amount of LINEAR kinetic energy that tells you how fast the ball moves along the plane, this kinetic energy conversion corresponds to a smaller linear velocity for the rotating ball relative to the sliding ball on a frictionless plane.

The total mechanical energy content, however, remains the same for both cases.

4. Oct 13, 2008

### cognaq

Thank you guys for you quick responses.
You helped me in some way, but I find it too difficult because of the rotational energy and the rotational friction coefficient, so I decided to rearrange the experiment a little bit (I am going to use blocks, and try to calculate the $$\mu$$).

I am going to write it here when I am done with planning, maybe you can then point out some mistakes. *going to work on it*

[edit: I decided to open a new topic and mark this as SOLVED (it is a quite different topic then)]

Last edited: Oct 14, 2008