# Merry go round torque

1. Sep 12, 2009

### kaite

A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 18 in 13.0 . Assume the merry-go-round is a uniform disk of radius 3.0 and has a mass of 760 , and two children (each with a mass of 21 ) sit opposite each other on the edge.

Calculate the torque required to produce the acceleration, neglecting frictional torque.

What force is required at the edge?

2. Relevant equations

torque= I alpha
w=2pi f
w=w0+alpha *t

3. The attempt at a solution

change f to w
w= 2pi *.3rev/sec w=1.8849
find alpha
w=w0+ alpha*t 1.8849=alpha*13 alpha = .144997

find I
I= .5 MR^2= 3609
torque= I alpha = 3609*.144997= 523 this answer was incorrect I do not know why I also tried it with I for a hoop the answer was 1046 but this answer was also incorrect if you can tell me where i messed but that would be very helpful thanks

2. Sep 12, 2009

### kuruman

Hi kaite, welcome to PF.

Please add units to all given numerical quantities and restate the problem. Without them it will be difficult to troubleshoot your work.

3. Sep 12, 2009

### kaite

A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 18 rpm in 13.0 . Assume the merry-go-round is a uniform disk of radius 3.0m and has a mass of 760 kg, and two children (each with a mass of 21kg ) sit opposite each other on the edge.

Calculate the torque required to produce the acceleration, neglecting frictional torque.

What force is required at the edge?

2. Relevant equations

torque= I alpha
w=2pi f
w=w0+alpha *t

3. The attempt at a solution

change f to w
find alpha
w=w0+ alpha*t 1.8849=alpha*13 alpha = .144997rad/s^2

find I
I= .5 MR^2= 3609 kg m^2
torque= I alpha = 3609*.144997= 523 N M this answer was incorrect I do not know why I also tried it with I for a hoop the answer was 1046 N M but this answer was also incorrect if you can tell me where i messed but that would be very helpful thanks

The question is what torque is required for this acceleration and what force is required at the edge?

4. Sep 12, 2009

### kuruman

Consider the children. They add to the moment of inertia of the system.

Forget the hoop. The problem specifically says that the merry-go-round should be considered as a disk.