Posted by Adam on .
A playground merry-go-round made in the shape of a solid disk, has a diameter of 2.63 m and a mass of 353.9 kg. Two children, each of mass 30.5 kg, sit on opposite sides at the edge of the platform. Approximate the children as point masses.
(a) What torque is required to bring the merry-go-round from rest to 26 rpm in 19.7 s?
(b) If two other bigger children are going to push on the merry-go-round rim to produce this acceleration, with what force magnitude must each child push?
From rotational kinematics (n=26rpm=26/60 rev/s)
2•π•n = ε•t
ε =2•π•n/t =2•π•26/60•19.7 =0.138 rad/s^2
Moment of inertia (platform + 2 point masses):
I = M•R^2/2 + 2•M•R^2 = (1.315)^2•(353.9/2 + 2•30.5) = 412 kg•m^2
Newton’s 2 Law for rotation
M=I• ε =412•0.138 = 56.8 N•m.
The torque of coupled forces is
M =F•r, where
r is the distance between the points where the forces are applied (here r =D)
F = M/D =56.8/2.63 = 149 N