What is the Method for Measuring Moment of Inertia in a Yo-Yo Prototype?

[F.Workman]

Homework Statement

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

http://www.twiddla.com/202992

 

[tiny-tim]

Welcome to PF!

Hi F.Workman ! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[F.Workman]

Um, where do I start? ^^

 

[ideasrule]

Start by drawing free-body diagrams on the disk and the falling mass. Write out Newton's second law for each (Newton's rotational second law for the disk), and try to use them to find a relationship between h and t.