Question

3. A dad pushes tangentially on a small hand-driven merry-go-round and accelerates it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge

Answer 1

Mass moment of inetia of system = I=0.5*560*2.5² + 2*25*2.5² = 2062.5 kg-m²

angular velocity acived in 10 seconds = 15*2*pi/60=1.57 rad/s

angular acceleration of merry go round = 1.57/10=0.157 rad/s²

Torque required = 2062.5*0.157=323.98 Nm

Force required at the edge =323.98/2.5=129.6 N