- #1

PhizKid

- 477

- 1

## Homework Statement

## Homework Equations

Angular momentum/fixed axis rotation

## The Attempt at a Solution

Hi guys. I'm having a bit of trouble visualizing what will happen so if you could first indulge me with the mechanics. Imagine there was no friction to begin with; since the force is acting on the rope wound around the circular axle, will the yo - yo only slide to the right or will it slide to the right + roll backwards due to the pulling of the rope that is wound around the axle? It seems like it should be the second if I try to imagine it (don't have a yo - yo with me unfortunately :[). Now, regardless of that, the center of mass velocity will be directed to the right I think; was only assuming this based on physical grounds that the yo - yo will slide to the right but if the pulling of the rope around the axle causes it to roll backwards then idk if it will slide to the right or not anymore so if someone could clarify this that would be great. Going with that assumption, the friction force would be directed to the left. The equations of motion are [itex]ma = F - f = F - \mu mg[/itex] and, this is another point I would like someone to clarify for me because I assumed that since we want it to roll without slipping the rotation must be directed clockwise so that the tangential velocity at the contact point (left) is directed opposite to the assumed CM velocity direction (right) but I'm not sure if I'm supposed to assume this a priori or if its somehow supposed to come out of the equations at the end so if someone could clarify this as well, [itex]-\frac{1}{2}mR^{2}\alpha = -\frac{1}{2}mRa = Fb - \mu mgR[/itex] and putting all this together gives [itex]F = \frac{3\mu mg}{(1 + \frac{2b}{R})}[/itex]. If you could clarify all the things I asked for that would be great. Thanks!