# Yo-yo physics

1. May 29, 2005

### Mr. Snookums

Physics project on the yo-yo. It's for bonus marks.

I need to calculate the angular momentum of a yo-yo when it leaves your hand. The hand represents an inclined plane which imparts the spin. I'm keeping it simple and won't involve friction.

What I'm trying to get at is the equation for acceleration down an inclined plane. I've drawn a free body diagram but I just can't get anywhere on it. Yo-yo's mass is 0.2kg, and the incline would be about 50 degrees, I guess.

mg for the yo-yo is 1.96N, theta is 50 degrees. How do I get the acceleration down the inclined plane?

We haven't covered inclined planes and angular momentum yet, it's not even in the curriculum. That's why it's a bonus project.

2. May 29, 2005

### Hyperreality

Does this problem involve friction?

Note the two cases

Case 1: No friction
If there is no friction, the yo yo carries no angular momentum. The acceleration is simply $$mg sin\theta$$

Case 2: Friction
This makes things a little bit more complicated. Friction actually create angular momentum, and it also create a moment about the yo-yo. In this case you will need to express friction in terms of the rotational inertia and the radius of the yo-yo.

Good luck

3. May 30, 2005

### OlderDan

This would make sense if you were talking about a disk other than a yo-yo. The post by Hyperreality points out that without friction there would be no angular momentum without friction. That would be true for any old disk, and friction would be needed to impart a rotation. But a yo-yo is a different thing. The string wound around the axle makes it impossible for the yo-yo to move without beginning to rotate. If you know the radius of the axle, and you give the yo-yo an initial velocity downward, you can determine the rate of rotation in terms of the velocity and the radius. You can also calculate the change in both velocity and angular velocity (and change in momentum and angular momentum) resulting from gravity acting on the yo-yo. The fact that so much of the yo-yo energy is rotational energy is what makes the yo-yo climb back up the string to your hand. If your yo-yo is a sleeper, and you throw it hard enough there will still be plenty of energy left to climb the string even after friction slows the rotation at the bottom.