Yo-Yo hovering: rotational motion and torque

[SonOfOle]

Homework Statement

A disk (yo-yo) of Radius R and mass m is attached to a weightless cord on the disk's edge. At time zero, the disk is released and a force upwards is applied to the upper end of the chord so that the center of mass of the disk does not move up or down. What must be the minimum length, L, of the cord wound around the disk at time t=0 if you wish to keep it hovering this way until time t after you release it?

Homework Equations

The Attempt at a Solution

I can't recall how the torque produces an upwards force on the disk. How does that work again?

Thanks in advance.

 

[tiny-tim]

I can't recall how the torque produces an upwards force on the disk. How does that work again?

Hi SonOfOle!

The torque doesn't produce an upwards force on the disk.

The upwards force comes from you, pulling the string.

That upwards force, together with the weight of the disc (along a different parallel line) produces the torque!

Hint: apply good ol' Newton's second law to find the upwards force.

Then calculate the torque. Then calculate the angular acceleration.

 

[SonOfOle]

ah, got it now. I got $$L=g t^{2}$$.

Thanks.