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# Couple rotational questions watch

1. At the moment, I'm set to fail physics, so take it easy with the explanations.

First question: two rough (i.e. when they're in contact, there's no slippage between them) solid cylinders, on a smooth surface, collide. What happens next?

Second question: an orbiting astronaut notices a ruler () stationary in the cabin, and gives it a sharp tap perpendicular to its length. It rotates once every 0.8s and the centre of mass moves away at 0.4 m/s. How long is the ruler?

I have absolutely no idea how to approach either of these, so any help would be appreciated. Thanks!
2. Are the questions exactly as presented? No further info?
1st question: as the cylinders are on a "smooth" surface, I take it they could be moving without rotating/rolling. I.e. slipping. This also means that any force from the smooth surface acts vertically through the c. of g. of the cylinder and cannot cause rotation or any change in the translational motion of the cylinders.
In any collision, total angular and linear momentum will be conserved. What happens next will depend on the initial state of rotation and translation of the two cylinders. I.E. one at rest, other moving but not spinning. Both moving and spinning etc. The coefficient of restitution between the two will also matter in as much as we don't know if the collision is elastic or not. Either way, angular and linear momentum will be transferred from one to the other due to the rough surfaces applying a force component that is tangential to the surface and a force that acts through the c of g.
Qu 2.
At what point along the ruler does the astronaut apply the force? The end?
If so, you can replace the force applied at that point by an equal one through the c of g together with a moment equal to that force times its perpendicular distance from the c of g.
The one produces rotational momentum Iw and the other translational momentum mv.
3. (Original post by Stonebridge)
Are the questions exactly as presented? No further info?
Oh, sorry, my bad. The second question is as given (although it's quite possible that it expects an algebraic rather than numerical answer), but the first has the information that one cylinder is stationary whilst the other is rotating with some angular velocity and moving toward the first with linear velocity . The question is to find the angular and linear velocities of each cylinger after collision.

In any collision, total angular and linear momentum will be conserved.
Thanks, I think I can make an attempt at this now. I just couldn't really figure why angular momentum need be conserved, but if it is, I'll just run with that.

If so, you can replace the force applied at that point by an equal one through the c of g together with a moment equal to that force times its perpendicular distance from the c of g.
I'll need to think about this, but thanks. I think I can see how this would work, but I'll need to actually try it.

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