Question

10 kids are riding on a merry-go-round. The merry-go-round has a radius of 3 m and a mass of 2000 kg, and it is spinning with an angular velocity of 2 rad/s. The kids are riding at the rim of the merry-go-round, and they each have a mass of 30 kg. All of the kids jump radially off the merry-go-round, all at the same time. What would the angular velocity of the merry-go-round be after the kids jump off?

Answer 1

Here we have given that,

Total mass of 10 kids m = 10 ×30 =300 kg

Mass of merry go round M = 2000kg

Radius or merry go round R = 3m

Initial angular velocity Wi = 2rad/s

Final angular velocity Wf = to be find.

Now from the conservation of angular momentum we have the relation as,

(1/2MR^2+mR^2)Wi=1/2MR^2ωf .......1

Here i we have to consider the merry go round as circular disk and then treat its moment of inertia.

NOw form equation 1 we will have...

Wf = (0.5 × 2000× 3^2 + 300× 3^2)× 2/0.5 × 2000× 3^2

= 2.6 rad /s

Hence the angular velocity of the merry-go-round be after the kids jump off is 2.6 rad/s