Answer:
(a) 1.09 kg m²
(b) 48.9 %
Explanation:
mass of skater, m = 51 kg
frequency when the arms are extended, f = 0.64 rev/s
frequency when the arms are in, f' = 0.95 rev/s
radius of cylinder when the arms in, r' = 17 cm
Moment of inertia of the body of skater when the arms in, I' = 0.5 x m x r'²
I' = 0.5 x 51 x 0.17 x 0.17 ² = 0.737 kg m²
(a)
By using the conservation of angular momentum
I x ω = I' x ω'
I x 2 x π x f = I' x 2 x π x f'
I x 0.64 = 0.737 x 0.95
I = 1.09 kg m²
Thus, the moment of inertia when the arms are in extended is 1.09 kg m².
(b)
Initial kinetic energy when the arms are extended, k = 0.5 x I x ω²
K = 0.5 x 1.09 x 4 x 3.14 x 3.14 x 0.64 x 0.64 = 8.8 J
Final kinetic energy when the arms are in, k' = 0.5 x I' x ω'²
K' = 0.5 x 0.737 x 4 x 3.14 x 3.14 x 0.95 x 0.95 = 13.1 J
Percentage change in kinetic energy
= 48.9 %
Thus, the percentage change in kinetic energy is 48.9 %.
