A stationary skater with a mass of 80.0 kg and a moment of inertia (about her ce

Question

A stationary skater with a mass of 80.0 kg and a moment of inertia (about her central vertical axis) of 3.00 kg-m2 catches a baseball with her outstretched arm. The catch is made at a distance of 1.00 m from the central axis. The ball has a mass of 145 g and is traveling at 20.0 m/s before the catch. (a) What linear speed does the system (skater + ball) have after the catch? (b) What is the angular speed of the system (skater + ball) after the catch? (c) What percentage of the balls initial kinetic energy is lost during the catch? Neglect friction with the ice.

Explanation / Answer

a) 0.145 x 20 = (80 + 0.145)v

v = 0.0362 m/s

b) mvr = I w

0,145 x 20 x 1 = (3 + 0.145 x 1^2 ) x w

w = 0.922 rad/s

c) % = [0.145 x 20^2 /2   - 80.145 x 0.0362^2 /2 - (3 + 0.145 x 1^2 ) x 0.922^2 /2 ] x100 / [ 0.145 x 20^2 /2 ]

= 95.21 %

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