I'm not sure the correct answer to this question.
14. A 2 m radius 100 kg disk-shaped merry-go-round is turning at 1.5 rad/s with a 50 kg child on
the rim. The child throws at 10 kg medicine ball in the direction of rotation at 10 m/s. What is the
rotational speed of the merry-go-round after the medicine ball leaves the kid's hands? a) 1.15
rad/s b) 1.25 rad/s c) 1.35 rad/s d1.45 rad's e) 1.55 rad/s
Solution
here,
radius , r = 2 m
mass of merry-go-round , m1 = 100 kg
mass of child , m2 = 50 kg
mass of medicine ball , m3 = 10 kg
v = 10 m/s
w0 = 1.5 rad/s
let the rotational speed be w
using conservation of angular momentum
(0.5 * m1 * r^2 + m2 * r^2 + m3 * r^2) * w0 - m1 * r * v = (0.5 * m1 * r^2 + m2 * r^2) * w
( 0.5 * 100 * 2^2 + 50 * 2^2 + 10 * 2^2) * 1.5 - 10 * 2 * 10 = ( 0.5 * 100 * 2^2 + 50 * 2^2) * w
solving for w
w = 1.15 rad/s
the angular speed is a) 1.15 rad/s