# Calculate the moment of inertia

1. May 13, 2014

### asdff529

1. The problem statement, all variables and given/known data
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)

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

3. 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

2. May 13, 2014

### Staff: Mentor

Try solving for v and ω.

3. May 13, 2014

### BiGyElLoWhAt

well lets 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 =]

4. May 13, 2014

### Staff: Mentor

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.

5. May 13, 2014

### 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?

6. May 13, 2014

### 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.

7. May 13, 2014

### Staff: Mentor

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

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

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

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