Required torque to accelerate a disk of a certain mass

In summary, the problem involved calculating the torque needed to accelerate a disk from 0 rpm to 6 rpm in 10 seconds. Using the mass moment of inertia formula for a disk with uniform mass, the moment of inertia was calculated to be 18 kg-m^2. Converting the angular velocity of 6 rpm to radians per second, the average angular velocity was found to be 0.628319 rad/s. The angular acceleration was then calculated to be 0.0628319 rad/s^2. Multiplying the angular acceleration by the moment of inertia, the torque needed was found to be 1.13097 N-m.
  • #1
Sum1
8
0

Homework Statement



(Actually, this is not a homework, but a project I'm trying to accomplish
but I have almost forgotten physics...)

There is a disk weighting 100kg with a radius of 0.6 meters. What would be the torque needed to accelerate the disk from 0 rpm to 6 rpm in 10 seconds?

Variables:

m=100 kg
r=0.6 meters
rpmA=0 rpm
rpmB=6 rpm
t=10 seconds

Homework Equations



If I'm not wrong:

The mass moment of inertia of a disk with a uniform mass is considered to be:
(m*r^2)/2
where m=mass, r= radius

Converting rpm to radians/sec:
rad/s = rpm * (pi/30)
where pi = 3.14159...


The Attempt at a Solution



So, trying to solve the problem:

moment of inertia of the disk
I = (m*r^2)/2
= (100*0.6^2)/2
= 18

Average angular velocity in radians per second
v = (rpmB-rpmA) * (pi/30)
= 0.628319

Angular acceleration in rad/s^2
a = Angular velocity in radians per sec /t sec
= v/t
= 0.0628319

Torque
T = Angular acceleration * Moment of Inertia
= a*I
= 1.13097

Is this correct?
Is the above result of Torque in Kg-m?
What exactly is the unit of the above inertia result? Is it Kg-m^2 ?

Any help will be appreciated!
 
Last edited:
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  • #2
Your method looks correct. I haven't checked your math. Note that rpmB-rpmA is not the average angular velocity. It is the change in angular velocity. In any case, that's what you want -- the change in angular velocity. That is because, for uniform acceleration, a = (change in v)/time.

Torque has units of Newton-metres.

1 N = 1 kg*m/s^2
1 Nm = 1 kg*m^2/s^2

Moment of inertia has units of kg*m^2...and multiplying by the angular acceleration to get torque gives you the missing 1/s^2.
 
  • #3
cepheid said:
Your method looks correct. I haven't checked your math. Note that rpmB-rpmA is not the average angular velocity. It is the change in angular velocity. In any case, that's what you want -- the change in angular velocity. That is because, for uniform acceleration, a = (change in v)/time.

Torque has units of Newton-metres.

1 N = 1 kg*m/s^2
1 Nm = 1 kg*m^2/s^2

Moment of inertia has units of kg*m^2...and multiplying by the angular acceleration to get torque gives you the missing 1/s^2.

cepheid, thanks for the reply!

Yes, it is the change in angular velocity not the average -that was stupid!

But I'm still confused about the output torque unit of the above calculation. On this site http://nmbtc.com/Calculators/converter.swf" it has Kg-m and N-m torque units. Should I consider the above result as N-m? If so, that would mean that it requires about 10 times less torque than if the output unit is Kg-m!
 
Last edited by a moderator:
  • #4
Nevermind, just found an example which used Kg and meters and the output torque unit was Newton meters! So it is N-m! :smile:
 

What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is often described as a twisting or turning force.

How is torque related to acceleration?

Torque is directly proportional to the angular acceleration of an object. This means that the greater the torque applied, the greater the acceleration will be.

What factors affect the required torque to accelerate a disk?

The required torque to accelerate a disk is affected by the mass of the disk, the radius of the disk, and the moment of inertia of the disk.

What is the formula for calculating required torque to accelerate a disk?

The formula for calculating required torque is T = I * α, where T is torque, I is moment of inertia, and α is angular acceleration.

How can I determine the required torque for a specific mass of disk?

To determine the required torque for a specific mass of disk, you will need to know the radius and moment of inertia of the disk. These values can be used in the formula T = I * α to calculate the required torque.

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