# Rotation: Yo-Yo

1. Nov 24, 2013

### Avi Nandi

1. The problem statement, all variables and given/known data

A Yo-Yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR$^{2}$/2 and the thickness of the string can be neglected. The Yo-Yo is released from rest. The center of the Yo-Yo descends distance h before the string is fully unwound. Assuming it reverses direction with uniform spin velocity, find the average force on the string when the Yo Yo turns around.

2. Relevant equations

v=bα v = linear velocity of the yoyo. α= angular velocity of the yoyo.

$\frac{1}{2}$Mv$^{2}$ + $\frac{1}{2}$Iω$^{2}$ = Mgh

3. The attempt at a solution

From the constraint equation and the energy conservation I calculated final ω. Now change in angular momentum is 2Iω. Now I can't find the average force from here.

2. Nov 24, 2013

### Simon Bridge

You are asked to assume a uniform spin velocity - since the rotation changes neither rate not direction (constant velocity) how does it change angular momentum?

What changes direction when the yo-yo reaches the bottom of the string?

You do have a problem with "average force" though ... what would this mean?