Question

Suppose that a merry-go-round, which can be approximated as a disk, has no one on it, but it is rotating about a central vertical axis at 0.2 revolutions per second. If a 100kg man quickly sits down on the edge of it, what will be its new speed? (A disk has a moment of inertia I=(1/2)mR2 , mass of merry-go-round = 200kg , radius of merry-goround=6m)

Answer 1

0.1 rev/s

Step-by-step explanation:

M = mass of the merry go round = 200 kg

R = radius of merry go round = 6 m

`I_(o)` = Moment of inertia of merry go round = (0.5) MR² = (0.5) (200) (6)² = 3600 kgm²

m = mass of the man = 100 kg

`I_(f)` = Moment of inertia of merry go round when man sits on it at the edge = (0.5) MR² + mR² = (0.5) (200) (6)² + (100) (6)² = 7200 kgm²

`w_(o)` = initial Angular speed of merry-go-round before man sit = 0.2 rev/s

`w_(f)` = Angular speed of merry-go-round after man sit = ?

Using conservation of angular momentum

`I_(o)`
`w_(o)` =
`I_(f)`
`w_(f)`

(3600) (0.2) = (7200)
`w_(f)`

`w_(f)` = 0.1 rev/s