Answer
52 kg.
Work Step by Step
There is no net external torque on the child-wheel system, so its net angular momentum is conserved.
$$L_{i}=L_{f}$$
$$I_{wheel} \omega_i = I_{wheel} \omega_f + I_{child} \omega_f $$
$$I_{wheel} \omega_i = I_{wheel} \omega_f + m_{child}R_{wheel}^2 \omega_f $$
$$(1260 kg \cdot m^2)(1.70rad/s) = (1260 kg \cdot m^2)(1.35rad/s)+ m_{child}(2.5 m)^2(1.35rad/s) $$
Solve for the mass of the child, 52 kg.
