Question

A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are

outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg, 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 66 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. What is her new angular velocity, in rev/s?

Answer 1

let
w1 = 1.0 rev/s
I1 = (I_cyllider + I_rods)

= (0.5*M*R^2 + 2*(m*l^2/12 + m*((l/2) + R)^2 )

= (0.5*40*0.2^2 + 2*(2.5*0.66^2/12 + 2.5*(0.33 + 0.2)^2 )

= 2.386 kg.m^2

I2 = 0.5*M*R^2

= 0.5*45*0.2^2

= 0.9 kg.m^2

w2 = ?

apply conservation of angular momentum

I2*w2 = I1*w1

w2 = I1*w1/I2

= 2.386*1/0.9

= 2.6 rev/s <<<<<<<<<<<-----------Answer