physics
posted by samantha on .
a yoyo of mass 440kg measuring 0.9m in radius was dropped from a platform 63m high. One end of the string was tied to the platform, so the yoyo unwinds as it descends. Assuming the axle of the yoyo has a radius of 0.2m, find the velocity of descent at the end of the fall. The acceleration of gravity is 9.81 m/s^2.

The velocity of the yoyo at any height is r*w, where w is the angular velocity and r = 0.2 m.
Assume the yoyo is a uniform disc, or pair of discs. Its moment of inertia is (1/2) M R^2, except for a small contribution for the axle, which we will have to ignore since they don't tell you its mass or length.
After dropping a distance H, the potential energy loss equals the kinetic energy gain.
M g H = (1/2)M V^2 + (1/2) I w^2
= (1/2)M V^2 + (1/4)M R^2*(V/r)^2
The mass M cancels out.
V^2 = g*H /[1/2 + (1/4)(R/r)^2] 
THANK YOU SO MUCH!!! :)