A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 16 rpm in 11.5 s. Assume the merry-go-round is a uniform disk of radius 3.0 m and has a mass of 790 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. 1)Calculate the torque required to produce the acceleration, neglecting frictional torque. 2)What force is required at the edge? I got 1400 for the force and it was wrong.

Did you get the torque correct in part (1) ? It equals the angular acceleration divided by the moment of inertia, including that due to the children.

The force required at the edge equals the required torque divicded by the radius, 3.0 m.

You need to say what your units of force are. Don't just give a number.

To solve this problem, we will use the principles of rotational motion and force.

1) To calculate the torque required to produce the acceleration, we can use the equation:

Torque = Moment of Inertia * Angular Acceleration

The moment of inertia of a uniform disk can be calculated as:

Moment of Inertia = (1/2) * Mass * Radius^2

Using the given values, we have:

Moment of Inertia = (1/2) * 790 kg * (3.0 m)^2
= 3547.5 kg·m^2

To find the angular acceleration, we can use the relationship between angular acceleration (α) and the change in angular velocity (Δω):

α = Δω / Δt

Given that the initial angular velocity (ω_i) is 0 rpm, the final angular velocity (ω_f) is 16 rpm, and the time interval (Δt) is 11.5 s, we can calculate the change in angular velocity:

Δω = ω_f - ω_i = 16 rpm - 0 rpm

Now, let's convert the values to rad/s:

Δω = 16 rpm * (2π rad/1 min) * (1 min/60 s)
≈ 5.307 rad/s

Substituting the values into the equation for torque, we get:

Torque = Moment of Inertia * Angular Acceleration
= 3547.5 kg·m^2 * (5.307 rad/s) / 11.5 s
≈ 1633.247 N·m

So, the torque required to produce the acceleration is approximately 1633.247 N·m.

2) To determine the force required at the edge, we can use the equation:

Force = Torque / Radius

Substituting the values we previously calculated, we have:

Force = 1633.247 N·m / 3.0 m
≈ 544.416 N

Therefore, the force required at the edge is approximately 544.416 N.

It seems that you obtained a different answer for the force. Please double-check your calculations to identify any mistakes made along the way.