Answer:
a) I = 1.44 Kg.m²
b) I = 3.12 Kg.m²
As rarm increases, her moment of inertia will increase.
Explanation:
Given
The skater's mass: M = 64 Kg
Mass of both arms: m = (M/8) = 64 Kg / 2 = 8 Kg
Mass of one arm: = marm = m/2 = 8 Kg / 2 = 4 Kg
Mass of her rest body: Mcyl = M - 2m = 64 Kg - 8 Kg = 56 Kg
rarm = 0.20 m
Rcyl = 0.20 m
Larm = 0.60 m
a) We apply the equation (Using the Steiner Theorem)
I = Icyl + Iarms
I = (Mcyl*Rcyl²/2) + 2*marm*rarm²
I = (56 Kg*(0.20 m)²/2) +2(4 Kg)(0.20 m)²
I = 1.44 Kg.m²
b) Suppose that the center of the mass of her outstretched arm is in the middle, so that the mass of the arm will be at a distance of 50 cm, then
rarm = 0.50 m
We apply the same equation, then
I = Icyl + Iarms
I = (Mcyl*Rcyl²/2) + 2*marm*rarm²
I = (56 Kg*(0.20 m)²/2) +2(4 Kg)(0.50 m)²
I = 3.12 Kg.m²
As rarm increases, her moment of inertia will increase.
