Angular speed, Inertia, and Kinetic Energy Please solve with steps. I have the s

Question

Angular speed, Inertia, and Kinetic Energy

Please solve with steps. I have the solution but it's confusing. (14%)

PHSCS 105: Introductory Applied Physics Question 12 An ice skater spins, with her arms outstretched, at an angular speed of 12.6 rad/s. When she brings her arms close to her body, she decreases her moment of inertia by 12%. Determine the percentage change in her kinetic energy. (Ignore friction on the skates.) Do increase or decrease? What is the explanation for this result? es her kinetic energy

Explanation / Answer

Angular momentum is given by :

L = I*W

where I = initial moment of inertia

W = initial angular speed

After decreasing her moment of inertia, new moment of inertia ,I' = 100 - 12 = 88 percent = 0.88*I

Let the final angular speed be W'

Now, conservation of angular momentum,

I*W = I'*W' <-------- initial angular momentum = final angular momentum

So,IW = 0.88*I*W'

So, W' = 1/0.88*W = 1.136*W

So, angular speed increases and by 1.136 - 1 = 13.6 percent

So, final Kinetic energy, KEf = 0.5*( I' )*( W' )^2

So, KEf = 0.5*(0.88*I)*(W/0.88)^2 = (0.5*IW^2)/0.88 = 1.136*KEi <------ KEi = initial kinetic energy = 0.5*I*W^2

So, Kinetic energy has also increased by 0.136 = 13.6 percent == 14 percent

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