Question

a merry-go-round in the park has a radius of 2.5 m and rotational inertia of 1000 kg*m^2. a child pushes the merry-go-round with a constant force of 50 N applied at a point tangent to the edge. a frictional torque of 12 N*m acts at the axle of the merry-go-round. what is the rotational acceleration of the merry-go-round while the child is pushing? at this rate, what will the rotational velocity of the merry-go-round be after 12 s if it starts from rest? how many times does the merry-go-round go around while the child is applying the force?

Answer 1

Torque responsible for moving the merry-go-round(MGR) = F*R = 50*2.5 = 125 N-m

Net torque, T = 125- 12 = 113 N-m

We know that,

T = I$\alpha$

113 = 1000*$\alpha$

$\alpha$ = 0.113 rad/s²

initial angular(rotational) velocity, w_o = 0 rad/s

using,

w = w_o + $\alpha$ *t

w = 0 + 0.113* 12

w = 1.356 rad/s

again,

using,

$\theta$ = w_o*t + 0.5*$\alpha$*t²

$\theta$ = 0 + 0.5*0.113*12²

$\theta$ = 8.136 radians = 1.294 rotations