6-7. An ice skater has a mass of 60 kg. With her arms out her moment of inertia

Question

6-7. An ice skater has a mass of 60 kg. With her arms out her moment of inertia about her center of mass is 20 kgm2. What would her moment of inertia be if she pulled her arms in and tucked up into a "cylinder" of radius 0.5 m? ,-208m (B. 5.2 kgm2 C. 7.5 kgm2 D. 10 kgm2 If she were rotating at an angular speed of 4 rad/s with her arms out, how fast would she rotate if she pulled her A. 4.6 kgm2 arms in and tucked up into a "cylinder" of radius 0.5m? A. 4 rad/s B. 7.2 rad/s C. 10.7 rad/s D. 13.4 rad/s

Explanation / Answer

Given

ice skater with mass m = 60 kg

initial angular speed w1= 4 rad/s , I1 = 20 kg m^2

final angular speed W2 = ? , I2 = ?

radiusof the cylinder is r = 0.5 m

moment of inertia when she pulled her arms in is I2 = mr^2/2 = 60*0.5^2/2 = 7.5 kg m2

from conservation of angular momentum  

L1 = L2

I1*W1 = I2*W2

20*4 = 7.5*W2 ==> W2 = 80/7.5 rad/s = 10.67 rad/s

6.7

the moment of inertia of the skater whe she pulled her arms in is moment of inertia of the cylinder rotating about the axis passing through the center is I = mR^2/2

I = 60*0.5^2/2 = 7.5 kg m^2

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