Question

30) A man of 80kg mass is standing on the rim of a circular platform of mass 200kg rotating about its axis.
The mass of the platform with the man on it rotates at 12.0 rpm. If the man now moves to centre of the
platform, the rotational speed would become
1) 16.5 rpm
2) 25.7 rpm
3) 32.3 rpm
4) 31.2 rpm​

Answer 1

Given:

The mass of the body is m=80 Kg

The mass of the circular platform of mass M=200 Kg

The rpm is w=12

To find:

The rotational speed  of the body

Solution:

The initial moment of inertia

I= 80r² + 200r²/2

I=180r²/2

The final moment of inertia

I=200r²/2

I'=100r²

The angular momentum is

Iw=I'w

Putting the above values

180×12=100×w

21.6=w

So the rotational speed is 21.6 rpm.