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 ball❝s initial kinetic energy is lost during the catch? Neglect friction with the ice.

Answer 1

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 %

Answer 2

m1v1 = MV

.145*20 = (.145+80)V

linear speed of the system V = 0.0362 m/s

b)

w1 = V/R = 20/1 = 20

I1w1 = IW

mr^2 * w1 = (3 + mr^2)W

angular speed of the system after the catchW = .922 rad/s

c)

v1 = 20

v2 = RW = .922 m/s

percentage lost = (v1^2 - v2^2)/v1^2 * 100 = 99.787 %