biomechanics - angular kinetics

Question

Hanyu wants to become the first figure skater to land a quadruple axel (4.5 rotations). Nicknamed “The Projectile”, he figures that he must achieve a maximal height of 0.8m and have an angular momentum of -70kg·m2/s for the clockwise jump. Assuming these values to be true, what moment of inertia must he generate to successfully complete the jump? [8 marks] Hint: you will need to use equations of linear motion to solve the problem.

Answer 1

Why we would know the angular momentum and need to solve the I rather than the other way around... Anyway, we can solve it as an exercise.

I may not be understanding the problem fully, but it seems like you can calculate time in the air (the usual calculation for leaving the ground with a velocity and getting to a given height:

t in the air = 2sqrt(2h/g) which is double the time it takes to drop from a height, h (rearranging d = 1/2 gt²)

I get .808 seconds. (a pretty decent hang time).

Given that we assume that this is a constant rotation process once he leaves the ground, you can solve for the angular velocity ω = 2πf f is the turns per second (frequency)

In this case ω = 2π(4.5 revs/.808 s) = 34.99 rads/ sec

We are given L, the angular momentum, and want I, the moment of inertia:

L = Iω or I = L/ω = 70 kg-m²/s / 34.99 rad/s = 2.0 kg-m²

Hope that helps.