# 2 balls, one rolling, one sliding down the same ramp. Which is faster at the bottom?

by Sockpirate
Tags: balls, faster, ramp, rolling, sliding
 P: 2 This isn't homework, but I thought that it's probably better in here, as it's a fairly quick question. OK, so I have 2 identical balls (exact same mass and radius). They rest on the same position on 2 identical slopes (same gradient) and begin to move down the ramps. The only difference is that one rolls down and one slides down (i.e. doesn't roll). Which one reaches the bottom with the greater speed? Assume that the effect of friction is negligible. OK, so obviously GPE is converted into kinetic energy. This should be the same for both balls, since they start at the same height. However, would I be right in saying that the rolling ball will move slower (if friction is negligible), as some KE will be rotational and not translational KE? If friction were not negligible (i.e. it actually had an effect) which one would be faster now? Intuition tells me the rolling ball will, but I can't think why. Anyway, thanks very much for the help! As I said, it's not homework, just something I'm interested in, but thought it'd probably fit better in this forum ^^
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P: 41,563
 Quote by Sockpirate Assume that the effect of friction is negligible.
But friction cannot be neglected in the case of rolling without slipping. Without friction, the ball wouldn't roll.

 OK, so obviously GPE is converted into kinetic energy. This should be the same for both balls, since they start at the same height. However, would I be right in saying that the rolling ball will move slower (if friction is negligible), as some KE will be rotational and not translational KE?
If you compare something that slides without friction down the ramp to something that rolls down the ramp, you are absolutely correct.

 If friction were not negligible (i.e. it actually had an effect) which one would be faster now? Intuition tells me the rolling ball will, but I can't think why.
I haven't done the calculation, but I imagine it would depend on the coefficient of friction. (Note that for the case of rolling without slipping, the speed down the ramp does not depend on the coefficient of friction, so long as it's enough to prevent slipping.)

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