5. A merry-go- round in the park has a radius of 1.8 m and a rotational inertia

Question

5. A merry-go- round in the park has a radius of 1.8 m and a rotational inertia of 900 kg.m2 . a child pushed the merry-go-round with a constant force of 80N applied at the edge and parallel to the edge. A frictional torque of 12 N.m acts at the axle of the merry-go-round.
a. What is the net torque acting on the merry-go-round axle?
b. What is the rotational acceleration of the merry-go-round?
c. At this rate, what will the rotation velocity of the merry-go-round be after 15s if it starts from rest?
d. What is the rotational acceleration of the merry-go-round if the child stops pushing after 15 s? how long will it take for the merry-go-round to stop turning?

Explanation / Answer

a) the net torque acting = torque applied due to child - frictional torque

                                     = F*r -f

                                   T net = 80*1.8 - 12 = 132 N.m

b) rotational acceleration:

                      T net = I

                        = Tnet / I = 132 /900 = 0.1467 rad/sec2

c) rotational velocity , = 0 +*t = 0 + 0.1467*15 = 2.2 rad/sec

d) if child stops pushing then Tnet = - frictional torque =-12

                    = Tnet / I = -12 /900 = -0.0133 rad/sec2

time it takes to stop

= 0 +*t

0 = 2.2 -0.0133 t

t=165.41 secs

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