Answer:
24.609375 kgm²
Explanation:
I = Moment of inertia of the merry go round
[tex]N_1[/tex] = Initial speed = 51 rpm
[tex]N_2[/tex] = Final speed = 17 rpm
m = Mass of child = 31.5 kg
r = Radius = 1.25 m
In this system the angular momentum is conserved
[tex]IN_1=(I+mr^2)N_2\\\Rightarrow I\times 51=(I+31.5\times 1.25^2)17\\\Rightarrow I\dfrac{51}{17}-I=31.5\times 1.25^2\\\Rightarrow 2I=49.21875\\\Rightarrow I=\dfrac{49.21875}{2}\\\Rightarrow I=24.609375\ kgm^2[/tex]
The moment of inertia of the merry go round is 24.609375 kgm²
