Question

You will estimate how much slower an ice skater would spin, if a can of soda dropped into her hand while she was spinning. You may model her body as a vertical cylinder of radius 20 cn abd nass 50 kg, spinning about a vertical axis. Assume that shes initially spinning 10 times per second, so that initially wi=20pis-1. Suddenly she is handed the soda can, which is small enough that we can model it as a point-like mass of .33kg, which she holds at a distance 60cm from the axis of rotation. (a) find nthe moment of inertia of the ice skater before the soda can drops in her hand. (b) find the moment of inertia of the point-like soda can relative to the axis about which the ice skater rotates. (c) find the total moment of inertia of the system consisting of the ice skater and the soda can. (d) find her angular velocity wf, after the soda can falls into her hand and (e) calculate the percentage difference, compared to her initial angular velocity wi.

Answer 1

Let us define:
skater A
can of soda B

(a) find nthe moment of inertia of the ice skater before the soda can drops in her hand.

the moment of inertia of the skater (cylinder) is:

where :

mass skater

radius skater

evaluated numerically

(b) find the moment of inertia of the point-like soda can relative to the axis about which the ice skater rotates

The moment of inertia for the soda is a point mass

  mass skater

radius skater

evaluated numerically

(c) find the total moment of inertia of the system consisting of the ice skater and the soda can

initial inertia moment is equal to

d) find her angular velocity wf, after the soda can falls into her hand and

The principle of conservation of angular momentum is met

  initial angular momentum

  end angular momentum
the moment of inertia is only the end of the skater

the following applies

replacing

evaluated numerically

(e) calculate the percentage difference, compared to her initial angular velocity wi.

%

finally 112%-100%=12%that is, the angular velocity increased by 12%