Moment of intertia and net work problem

[keylostman]

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?

 

[Doc Al]

Find the change in her kinetic energy.

 

[keylostman]

I2W2-I1W1, where W is squared?

This equation i use correct ?

 

[Doc Al]

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

 

[keylostman]

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

 

[Doc Al]

1/2IW^2 ?

Right.

I thought Work done would be final work - intital work,

The work done will equal the change in energy.

 

[keylostman]

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

 

[keylostman]

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]

Looks good.