Calculate the moment of inertia of a skater given the following information.
(a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius.
(b) The skater with arms extended is approximately a cylinder that is 74.0 kg, has a 0.150 m radius, and has two 0.750 m long arms which are 3.00 kg each and extend straight out from the cylinder like rods rotated about their ends.

(a) If you consider the shape of the skater as approximately a cylinder, you use the following formula to calculate the moment of inertia of the skater:

[tex]I_s=\frac{1}{2}MR^2[/tex] (1)

M: mass of the skater = 60.0 kg

R: radius of the cylinder = 0.110m

[tex]I_s=\frac{1}{2}(60.0kg)(0.110m)^2=0.363kg.m^2[/tex]

The moment of inertia of the skater is 0.363 kgm^2

(b) In the case of the skater with his arms extended, you calculate the moment of inertia of a combine object, given by cylinder and a rod (the arms) that cross the cylinder. You use the following formula for the total moment of inertia:

[tex]I=I_c+I_r\\\\I=\frac{1}{2}M_1R^2+\frac{1}{12}M_2L^2[/tex] (2)

M1: mass of the cylinder = 74.0 kg

M2: mass of the rod = 3.00kg +3.00kg = 6.00kg

L: length of the rod = 0.750m + 0.750m = 1.50m

R: radius of the cylinder = 0.150

[tex]I=\frac{1}{2}(74.0kg)(0.150m)^2+\frac{1}{12}(6.00kg)(1.50m)^2\\\\I=1.95kg.m^2[/tex]

The moment of inertia of the skater with his arms extended is 1.95 kg.m^2