A 2.4-m-diameter merry-go-round with a mass of 270 kg is spinning at 20 rpm. John runs around the merry-go-round at 5.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 34 kg. Part A Part complete What is the merry-go-round's angular speed, in rpm, after John jumps on?

23.98 rpm

Explanation:

d = diameter of merry-go-round = 2.4 m

r = radius of merry-go-round = (0.5) d = (0.5) (2.4) = 1.2 m

m = mass of merry-go-round = 270 kg

I = moment of inertia of merry-go-round

Moment of inertia of merry-go-round is given as

I = (0.5) m r² = (0.5) (270) (1.2) ² = 194.4 kgm²

M = mass of john = 34 kg

Moment of inertia of merry-go-round and john together after jump is given as

I' = (0.5) m r² + M r² = 194.4 + (34) (1.2) ² = 243.36 kgm²

w = final angular speed

w₀ = initial angular speed of merry-go-round = 20 rpm = 2.093 rad/s

v = speed of john before jump

using conservation of angular momentum

Mvr + I w₀ = I' w

(34) (5) (1.2) + (194.4) (2.093) = (243.36) w

w = 2.51 rad/s

w = 23.98 rpm