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Consider a cylinder rolling in the forward direction with velocity of $v$ and angular velocity of $v/r$. There is a wall in front and the cylinder collides with the wall. The collision is perfectly elastic.

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Here I am unable to judge what will happen next. Will it stop pure rolling and moves in translational for a while, or will it continue to pure roll in opposite direction after the collision?

Qmechanic
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JAZZ
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1 Answers1

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It should stop rolling instantaneously and then start rolling in the opposite direction.

When the cylinder collides with the wall, the point on the cylinder's surface in contact with the wall is moving instantaneously in the downward direction. Elastic collisions reverse velocities, so the instant after the collision, the velocity of that point becomes diametrically upward. Same thing happens with the translational velocity. Before the collision, the velocity of the center-of-mass of the cylinder is left-to-right, whereas after, it is right-to-left. The overall motion is such that the rolling reverses, with the cylinder at rest very briefly before the motion flips.

Yejus
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  • If there appears a force pointing upwards at the point of contact – Guillermo BCN Jun 07 '21 at 05:35
  • Sorry, I posted by accident before: I meant to say that the relative velocity at the point of contact is not in fact vertical but rather forma a 45-degree angle with either wall, as the cylinder is translating as it rolls. Note that, after the impact, the cylinder may be phshed up and even lose contact with the bottom wall if it moves at a fast enough rate. – Guillermo BCN Jun 07 '21 at 05:45
  • @GuillermoBCN Hmm, I was splitting the motion into rotation + translation. The total relative velocity may be slanted, but shouldn't the rotational component of the velocity be vertical to the wall (ignoring the COM component)? – Yejus Jun 07 '21 at 08:22