A child pushes tangentially on a small hand driven merry- go- round. She is able to accelerate it from rest to 20 rpm in 10 s. Modeling the merry go round as a uniform disk of radius 3.5 m and mass 800 kg, find the torque required to produce that acceleration. Neglect the frictional torque.

Question

A child pushes tangentially on a small hand driven merry- go- round. She is able to accelerate it from rest to 20 rpm in 10 s. Modeling the merry go round as a uniform disk of radius 3.5 m and mass 800 kg, find the torque required to produce that acceleration. Neglect the frictional torque.

Answer 1

now use your text and try to do the problems

torque = rate of change of angular momentum
= change in I omega/ change in time

initial omega = 0
final omega = 20 *2 pi /60 radians/second

Your text has a table of moments of inertia of shapes certainly including a solid disk with axis through the center like a wheel.
This is the last one I will help with. You are not trying.

Answer 2

To find the torque required to produce the acceleration of the merry-go-round, we can use the following equation:

Torque = Moment of inertia * Angular acceleration

To calculate the moment of inertia, we need to know the formula for the moment of inertia of a uniform disk, which is given as:

I = (1/2) * m * r^2

where
I is the moment of inertia,
m is the mass of the disk, and
r is the radius of the disk.

In this case, we are given:
m = 800 kg
r = 3.5 m

Substituting these values into the equation, we can calculate the moment of inertia:

I = (1/2) * 800 kg * (3.5 m)^2

Next, we need to find the angular acceleration. The angular acceleration is given by the change in angular velocity divided by the time taken:

Angular acceleration = (Final angular velocity - Initial angular velocity) / time

In this case:
Final angular velocity = 20 rpm
Initial angular velocity = 0 rpm
time = 10 s

To convert the final and initial angular velocities to radians per second, we use the conversion factor: 1 revolution = 2 * pi radians

So, the final angular velocity in radians per second is:
20 rpm * (2 * pi radians / 1 revolution) * (1 minute / 60 seconds) = (40 * pi / 3) rad/s

The initial angular velocity is 0 rad/s.

Substituting these values into the formula for angular acceleration, we can calculate it.

Finally, we can calculate the torque by multiplying the moment of inertia by the angular acceleration:

Torque = Moment of inertia * Angular acceleration

Substituting the calculated moment of inertia and angular acceleration, we can find the torque required to produce the given acceleration.