Kristen is spinning on the ice at 40 rad/s about her longitudinal axis when she abducts her arms and doubles her radius of gyration about her longitudinal axis from 32 cm to 64 cm. If her angular momentum is conserved, what is her angular velocity about her longitudinal axis after she increases her radius of gyration (in rad/s)

Answer: I = k^2m ... equa1

I = moment of inertia

M = mass of skater

K = radius of gyration.

When her angular momentum is conserved we have

Iw = I1W1 ... equ 2

Where I = with extended arm, w = angular momentum = 40rads/s, I1 = inertia when hands her tucked in, w1 = angular momentum when hands are tucked in.

Substituting equation 1 into equ2 and simplifying to give

W = (k/k1) ^2W ... equation 3

Where'd k = 64cm, k1 = 32cm, w = angular momentum when hands is tucked in = 40rad/s

Substituting figures into equation 3

W1 = 10rad/s

Explanation:

Assuming a centroidal axis of the skater gives equation 1