Question

A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.600 rev/s. What is its angular velocity (in rev/s) after a 25.0 kg child gets onto it by grabbing its outer edge

Answer 1

The final velocity
`\omega_f = 0.4235 (rev)/(s)`

Step-by-step explanation:

Given data

Mass of merry go round
`M_m` = 120 kg

Radius = 1.8 m

Initial angular velocity
`\omega_i` = 0.6
`(rev)/(sec)`

Mass of boy
`M_(boy)` = 25 kg

We know that the final velocity is given by

`\omega_f = ((1)/(2)M_m \omega_i )/(M_(boy) + (1)/(2) M_m )`

Put all the values in above formula we get

`\omega_f = ((1)/(2)(120) 0.6)/(25 + (1)/(2) (120) )`

`\omega_f = 0.4235 (rev)/(s)`

This is the final velocity.