Question

Canadian Olivia Oliver broke the Guinness World Record for the fastest spin on ice skates on January 2015 with an angular velocity of 342 rpm. Going into the spin, her arms and left leg are extended outwards and she spins at about 130 rpm. Then to speed up, she draws her arms and leg inwards, decreasing her moment of inertia. (A) What is the ratio of the moment of inertia before pulling in her arms and legs to the point where she is spinning fastest? (B) To achieve a final angular velocity of 375 rpm, how much faster would her initial an- gular velocity have to be?

Answer 1

Answer:

a) 2.63 : 1

b) 143.13 rpm

Explanation:

initial angular velocity ω' = 130 rpm

final angular velocity ω = 342 rpm

recall that angular momentum = ωI

where I is the moment of inertia.

for the initial spinning condition, we take moment of inertial = I'

for final spinning condition, we take moment of inertia = I

initial angular momentum = ω'I' = 130 I'

final angular momentum = ωI = 342 I

according to conservation of angular momentum, initial angular momentum must be equal to the final angular momentum, therefore

342 I = 130 I'

ratio of initial moment of inertia to final moment of inertia = I'/I

==> I'/I = 342/130 ≅ 2.63 : 1

b) to achieve a final angular velocity of of 375 rpm, her initial velocity will have to be

2.63 = 375/ω'

ω' = 375/2.63 = 143.13 rpm