Calculating the Torque for a Hand-Driven Merry-Go-Round

[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?

Homework Equations

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

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

 

[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.

 

[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. Homework 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 rad/sec
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?

 

[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.