Rolling vs. Sliding: Which Ball Reaches Bottom Faster?

[Sockpirate]

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 ^^

 

[Doc Al]

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.)

 

[kerimek]

I would approach this question by first considering the basic principles of physics involved. In this scenario, both balls have the same mass and radius, and are starting at the same height on identical slopes. This means that they both have the same potential energy at the start.

When the balls start moving down the slope, this potential energy is converted into kinetic energy. However, as you mentioned, the rolling ball will have both translational and rotational kinetic energy, while the sliding ball will only have translational kinetic energy.

In terms of energy conservation, the total kinetic energy of the rolling ball will be equal to the total kinetic energy of the sliding ball. However, the distribution of this kinetic energy may be different.

Intuitively, we may think that the rolling ball will move slower because some of its kinetic energy is being used for rotational motion. However, this is not necessarily the case. In fact, the rolling ball may actually reach the bottom faster than the sliding ball.

This is because the rolling ball has a lower center of mass compared to the sliding ball. This means that the rolling ball has a lower potential energy at any given point on the slope, and therefore, can convert this energy into kinetic energy more efficiently.

If we were to introduce friction into the scenario, it would also have a different effect on the rolling and sliding balls. Friction would cause both balls to lose some of their kinetic energy, but the rolling ball would still have a lower center of mass and therefore, would be able to maintain a higher speed compared to the sliding ball.

In conclusion, while it may seem counterintuitive, the rolling ball may actually reach the bottom faster than the sliding ball in this scenario. However, the exact outcome would depend on the specific conditions, such as the slope gradient and the amount of friction present.