A2.4-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

its c i just checked it

energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this