Trouble with exam prep question

Dec 2017
7
0
A stationary horizontal platform is free to rotate about its vertical axis. The radius of the platform is R=1.6m and its moment of inertia is 660 kgm^2. A 43kg boy jumps on the rim of the platform with the velocity of 2.2 m/s tangential to the rim. What will be the angular speed of the platform with the boy?

I am helping my son prep for an exam. We have been given the answer of w=.197 rad/s, but we cannot figure out how that is correct.

We have considered rotational kinetic energy of the platform and of the boy along with conservation of momentum, but no luck.

Any assistance would be greatly appreciated. I am not a physics expert and can only help him so much.
 
Apr 2017
537
138
The addition of the boy to the platform will change it's I to 660 + (43 x 1.6 x 1.6)

The new I is 770

Initial energy in boy = 1/2 x 43 x2.2 x2.2 = 104 = 1/2 x 770 x (omega squared)

Omega squared= 0.3106

Omega = 0.557 rad/sec