Jacob and Sophia are playing with a merry-go-round on a playground. The merry-go-round can be modeled as a flat disk with massM= 223.0kg and radiusR= 3.3 m that freely rotates horizontally without frictionabout its center axis. When the merry-go-round is already spinning at23 rotations per minute, Jacob exerts a constant forceFJ= 12.3 Ntangent to the outer edge of the merry go round in the direction of themerry-go-round’s rotation. At the same time Sophia puts her foot ata distancer= 3.1 m from the center, which exerts a constant force offrictionFS= 21.2 N. How long will it take for the merry-go-round tocome to a stop?

116 s

Explanation:

We can convert the 23 rotation per minute to radian per second knowing each rotation is 2π and each minute has 60 seconds.

The torque generated by Jacob at the outer rim in the direction of motion

The torque generated by Sophia at r = 3.1 m that hampers the motion is

The net torque is

The moment of inertia of the solid disk merry-go-round is:

Where m = 223 kg is the disk mass and R = 3.3 m is the radius of the disk.

So the angular deceleration is

If the initial angular speed is 2.41, the time it'd take to decelerate to rest is

seeing the graph would

the total distance traveled by the car is

30km + 49km = 79 km .