Calculate the moment of inertia

[asdff529]

Homework Statement

A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r.
Assume there is no friction.The mass is released from rest and falls a distance S after time t.
Find the moment of inertia of the axle.(represents I in terms of m,r,t and S)

Homework Equations

work done by moment=0.5Iω^2
v=at
S=0.5at^2

The Attempt at a Solution

my final equation is as follows
TS=0.5Iω^2,where T is the tension
v=at=rαt where α is the angular acceleration
(mg-T)S=0.5mv^2
but i can't reach the requirement
maybe there are lots of error inside and sorry for my poor english

 

[Doc Al]

Try solving for v and ω.

 

[BiGyElLoWhAt]

A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r.
Assume there is no friction.The mass is released from rest and falls a distance S after time t.
Find the moment of inertia of the axle.(represents I in terms of m,r,t and S)

well let's look at what's happening...
You have a mass on an axel, and you release it, the Earth (gravity) exerts a torque of $T = I\dot{\omega}$ on the axel and it accelerates angularly at a rate of $\dot{\omega}$

So I guess what it boils down to is this: how else can you define $T$?
There's another definition that involves 2 things that you are given (variables) and a constant that you know.

Answer this and we'll go from there.

PS I like this problem =]

 

[Doc Al]

There are several ways to solve this. There is nothing wrong with the original approach using work and energy. The only thing to realize is that v and ω are not unknowns--a little kinematics is all you need to find them.

 

[asdff529]

i almost forgot i can use the formula v^2-u^2=2as
so v=sqrt(2rαS) ?
and ω=αt or ω=v/R
am i going right?

 

[BiGyElLoWhAt]

what's u?
Also you're over complicating it in my opinion.
Start out with what you know, write out some definitions, and when in doubt: N2L is god.

 

[Doc Al]

i almost forgot i can use the formula v^2-u^2=2as
so v=sqrt(2rαS) ?
and ω=αt or ω=v/R
am i going right?

First step is to find the acceleration. You had the formula in your first post.

S=0.5at^2

Then find v. Again, you had the formula in your first post.

v=at

Given v, you can find ω since they are related.

Then you can use the energy equations you wrote in your first post.