Why Does Angular Velocity Appear Opposite to Linear Velocity?

[Fascheue]

I’m not quite sure where to put this post so forgive me if it’s misplaced, but can somebody explain why the angular velocity in the picture here appears to be in the opposite direction as I would expect if the velocity is in the direction that is is.

I’m not looking to solve this problem (that’s why I didn’t post this in the homework thread), I’m just wondering why the angular velocity is counter-clockwise and the velocity is to the right.

 

[jbriggs444]

The problem statement talks about the coin coming to rest (both translationally and rotationally). That can only work out if the coin is launched with back-spin. The diagram shows back-spin.

It is amusing to launch a hula hoop, giving it a backward flick of the wrist at release so that it spins backward. With a little practice one can arrange for the forward progress and the backward spin to cancel out at nearly the same time, whereupon the hoop falls to the ground.

Video:

 

[kuruman]

The coin is sliding relative to the surface of the table while it's moving to the right. This is the case when ω > V/R and the coin is given an impulse to the right. The situation is analogous to striking a cue ball with "backward english" meaning that the ball is struck sharply below center at the six o' clock position.

 

[Fascheue]

The problem statement talks about the coin coming to rest (both translationally and rotationally). That can only work out if the coin is launched with back-spin. The diagram shows back-spin.

It is amusing to launch a hula hoop, giving it a backward flick of the wrist at release so that it spins backward. With a little practice one can arrange for the forward progress and the backward spin to cancel out at nearly the same time, whereupon the hoop falls to the ground.

Video:

Okay I thought that might be it, it just seems a bit unusual.

Why is it the case that the coin can only come to rest translationally and rotationally if it is launched with backspin? If you roll a coin forward does it not have forward velocity and clockwise spin that simultaneousley come to rest?

 

[A.T.]

Why is it the case that the coin can only come to rest translationally and rotationally if it is launched with backspin?

Because the question implicitly only considers kinetic friction.

If you roll a coin forward does it not have forward velocity and clockwise spin that simultaneousley come to rest?

That requires rolling resistance and/or air drag, which are to be neglected here, as no parameters on them are given.

 

[sophiecentaur]

it just seems a bit unusual.

Yes. it is an unusual problem, which is what makes it interesting. It is actually easier to solve than a problem in which the coin is rolling naturally because the kinetic friction is an easier concept than 'rolling' resistance.
One can worry too much about the motives of the people who set problems. The motives are often questionable and it's often best to get on and just answer the problem as stated.