In testing a design for a yo-yo, an engineer begins by constructing a simple prototype--a string wound about the rim of a wooden disk. She puts an axle riding on nearly frictionless ball bearings through the axis of the wooden disk and fixes the ends of the axle. In order to measure the moment of inertia of the disk, she attaches a weight of mass m to the string and measures how long it takes to fall a given distance.
a) assuming the moment of inertia of the disk is given by I, and the radius of the disk is R, find the time for the mass to fall a distance h, starting from rest.
b) She doesn't have a very accurate stopwatch, but she still wants to get a measurement good to a few percent. She decides a fall time of 2 seconds would work. How big a mass should she use? Imagine you were setting up this experiment and make reasonable estimates of the parameters you need.
I = 0.5MR2