# Moment of intertia and net work problem

A ballerian spins initially at 1.5rev/s when arms are extended. She then draws in her arms to her body and her moment of intertia is .88kg m^2 and her angular speed increases to 4.0rev/s. Determine the network she did to increase her angular speed?

To find moment of inertia was pretty simple i used IW=I2W2 for and solved for I, I(1.5rev/s * 2PI rad/1rev)=(.88kg m^2)(4.0rev/s * 2PI rad/1rev) and i got 2.3kg M^2. Ok this was fairly easy. But for Net WORK, how do i calculate it ? I am not to sure which equation to use.... Is it Sum of Net WORK= I2W2-I1W1, where W is squared?

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Doc Al
Mentor
Find the change in her kinetic energy.

I2W2-I1W1, where W is squared?

This equation i use correct ?

Doc Al
Mentor
No. (It's almost right.) You used the correct equation for KE in your other thread.

1/2IW^2 ? I thought Work done would be final work - intital work,

Doc Al
Mentor
1/2IW^2 ?
Right.
I thought Work done would be final work - intital work,
The work done will equal the change in energy.

so its then .5 * .88 * (4.0 * 2pi) ?

W = (1/2) (.88)(25.13)^2 - (1/2)(2.3)(9.42)^2

W =((1 / 2) * .88 * (25.13^2)) - ((1 / 2) * 2.3 * (9.42^2)) =
W= 175.820576 joules

this is what i did, and i believe it rights, makes sense

Doc Al
Mentor
Looks good.