A merry go round in the park has a radius of 1.8 m and a rotational inertia of 900 kg-m^2. A child pushes the merry go round with a constant force of 80 N applied at the edge and parrallel to the edge. A frictional torque of 12 Nm acts at the axle of the merry go round. What is the rotational acceleration of the merry go round if the child stops pushing after 15 seconds? How long will it take for the merry go round to stop turning?

Question

A merry go round in the park has a radius of 1.8 m and a rotational inertia of 900 kg-m^2. A child pushes the merry go round with a constant force of 80 N applied at the edge and parrallel to the edge. A frictional torque of 12 Nm acts at the axle of the merry go round.  What is the rotational acceleration of the merry go round if the child stops pushing after 15 seconds?  How long will it take for the merry go round to stop turning?

drwls · Accepted Answer

After the child stops pushing, the rotational acceleration is negative. it slows down.
Use the equation
alpha = L/I
where alpha is the angular DEceleration, I is the moment of inertia and L is the frictional torque.

To determine how long it takes to stop. you need to calculate how fast it is going when the pushing force stops. That is a somewhat harder problem, but uses the same equation. You need to calculate the angular acceleration rate while it is being pushed, and multiply that by the time (15 seconds).

Use the same L/I equation, but in this accvelerating case, the torque is the difference of the pushing and frictional torques.