# Derivation of alternative inertia equation, I'm close but one bits not working

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#1
This question is more engineering than physics however I was hoping someone could help me.

The help sheet we have been given hints to us that the for 1/t^2 = km the k=(gr^2)/(2is) (where i is inertia.).

I have managed to derive very nearly that equation, however for me I just get r instead of r^2. Here is my method, if you see any errors it would be brilliant if you could point them out.

For our experiment we have a spindle with a string wound round it and a mass attached to the end, on the other end of the spindle is a larger disc (we are measuring the inertia of).

the torque applied = mass dropped x g x radius of spindle = mgr
To use the equation inertia = T/acel we obvs need aceleration. this can be got using suvat s= ut+1/2 at^2 where ut = 0 s= distance fallen of mass and t = time measured to do so.
this ends up with acel = 2s/t^2

so inertia = (mgr)/(2s/t^2)
which then rearranges to
1/t^2 = km where k = gr/2is no r^2 I'm struggling to work out whether its a typo in the sheet or me being a moron somehow, a few other people have just skipped this part of the report or not derived it, however from what the requirements say I'm thinking they want us to derive it.
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5 years ago
#2
(Original post by lbsf1)

the torque applied = mass dropped x g x radius of spindle = mgr
To use the equation inertia = T/acel we obvs need aceleration. this can be got using suvat s= ut+1/2 at^2 where ut = 0 s= distance fallen of mass and t = time measured to do so.
this ends up with acel = 2s/t^2

so inertia = (mgr)/(2s/t^2)
which then rearranges to
1/t^2 = km where k = gr/2is no r^2 I'm struggling to work out whether its a typo in the sheet or me being a moron somehow, a few other people have just skipped this part of the report or not derived it, however from what the requirements say I'm thinking they want us to derive it.
The acceleration you need in the Torque=moment of inertia x accel formula (highlighted) must be angular acceleration.

The suvat formula you have used has just calculated the linear acceleration of the mass, not the angular acceleration of the disc.
You need to divide the linear acceleration by r to find the angular accel.
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