Final answer:
To calculate the time to give the merry-go-round an angular velocity of 1.50 rad/s, and the time to stop it with an applied force, one would need the angular acceleration and deceleration, which are not provided. The number of revolutions to generate an angular velocity of 1.50 rad/s is approximately 0.23873241463.
Step-by-step explanation:
To address the various aspects of calculating the effect of mass distribution on a merry-go-round, several physics concepts must be applied, especially those related to angular motion and torque.
(a) Time to reach an angular velocity of 1.50 rad/s
The time it takes for the father to give the merry-go-round an angular velocity of 1.50 rad/s can be calculated using the formula for angular acceleration (α = Δω / Δt) where Δω is the change in angular velocity and Δt is the change in time. Unfortunately, without knowing the angular acceleration the father provides, this cannot be calculated.
(b) Revolutions to generate the angular velocity
To find the number of revolutions needed to reach the angular velocity, one must divide the angular velocity by the conversion factor from radians per second to revolutions per second (1 rev = 2π rad). Therefore, 1.50 rad/s is equivalent to approximately 1.50/2π or about 0.23873241463 revolutions.
(c) Time to stop the merry-go-round with a force
If the father exerts a slowing force, the resulting torque (τ = F * r) can be used to find the angular deceleration assuming a constant force. With the angular deceleration and the initial angular velocity, one can use the same angular formula (α = Δω / Δt) to calculate the time required to stop the merry-go-round. In this case, without the moment of inertia or existing angular acceleration to calculate deceleration, this cannot be determined.