# Relationship between torque, speed, and mass (Need Help Quickly!)

Discussion in 'Physics' started by Management, Oct 17, 2009.

1. ### Management Thread Starter Active Member

Sep 18, 2007
306
0
Hi,

I am having a hard time understanding the relationship between torque, angular speed, & required mass of an object. Angular accerlation notwithstanding.

Can someone help me understand how the ability of a machine to spin faster reduces the requirement for torque to generate a specific power and then subsequently reduces the necessary mass of the rotating object?

I am really concerned of the latter part and how it relates to sizing an electrical machine. Thanks.

Apr 5, 2008
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3. ### steveb Senior Member

Jul 3, 2008
2,433
469
The first question is straightforward and has a very simple answer. Power is torque times angular speed. Hence for a given mechanical power constraint, less torque is needed when the speed is faster.

The second question is less clear to me, but perhaps you are referring to the stored kinetic energy in the spinning mass. The kinetic energy is 0.5*J*w^2 where J is the moment of inertia of the spinning armature and w is the angular speed. Note that it's not the mass, but the moment of inertia that is important here. If an object is spinning faster, then you need less inertia to maintain a certain stored kinetic energy in the system. The stored energy is useful to reduce the effect of transient electrical or mechanical perturbations on the system.

Last edited: Oct 17, 2009
4. ### Management Thread Starter Active Member

Sep 18, 2007
306
0
So the equation for J (inertia) is mass times the radius squared. So you can't really calculate for the reduction in mass. Well unless you keep the radius constant, correct?

5. ### Management Thread Starter Active Member

Sep 18, 2007
306
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So ok, what if you have a gas turbine shaft that has a moment of inertia x. You are driving it with a motor (directly coupled). Does the moment of inertia of the motor have to be the same to be able to drive the turbine shalft. Meaning you have control over the sizing of the motor and you know you want to drive the turbine at a specific speed, lets call it v.

6. ### steveb Senior Member

Jul 3, 2008
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469
Well, the formulae for J varies depending on the shape and density distribution of the object, but your equation captures the basic effect. Mass that is out at a further radius has a large affect on J, given the square law dependence. However if you maintain a similar shape and density distribution, you can reduce the mass as the speed increases.

7. ### steveb Senior Member

Jul 3, 2008
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I don't think the motor moment of inertia is critical here. The total inertia from the motor armature and the gas turbine will be relevant for the basic system performance.

Perhaps in very advanced calculations related to flexing/stress on the mechanical coupling, you would care about the finer details.

8. ### Management Thread Starter Active Member

Sep 18, 2007
306
0
Thank you. Your a great resource.

The reason I am asking these questions is because I am trying to justify why using a direct coupled configuration of a turbine to a "generator" results in the reduction of the mass. The direct coupling results in approx. a 9.2 times increase in generator rotational speed. I'm trying to come up with a line of reasoning that states that the mass would reduce by x amount.

Is there a direct equation I can write that shows this.

I know:
power = torque * angular speed
torque = moment of inertia * angular acceleration
kinetic energy = 1/2 * moment of inertia * angular speed^2 (from steveb)
moment of inertia = mass * radius^2 (mass of the magnet a radius r from the center shaft)

The thing is I don't know what the previous mass is or teh radius that it was away. I just have to come up with amount that would be reduced. And then size a distance r and approx mass based on other things in the machine. If you're willing to assist it would be great.

9. ### steveb Senior Member

Jul 3, 2008
2,433
469
I'm not sure I can add much more help without details of the applications and the devices involved. As a general rule, I would say don't add mass needlessly. So we would want to know why mass is needed in the first place. There is always a minimum mass needed for structural performance, but adding mass beyond this just adds friction as slows down the spin-up and spin-down time. Adding mass beyond that is usually done to create a flywheel that stores mechanical energy. Greater speed would mean that less mass is needed for energy storage, but without knowing the application, it's not clear that this flywheel effect is relevant. So again, we need to know why mass would not be minimized in the first place. If mass is minimized in the first place, then the higher speed system is likely to break something, and maybe you need to add more mass for strength.

It seems like you are looking for a basic general principle that allows you to make a broad statement about reducing mass. It also seems that you know that this rule is valid and you are just looking for the explanation. However, nothing in particular is coming to my mind for the general case. If you can provide more details, maybe you'll trigger a key thought that leads to the answer for a more specific situation.

10. ### RimfireJim Member

Apr 7, 2008
22
2
Management, are you perhaps talking about "reflected inertia", which comes into play for control systems for motors driving a load through a speed increaser or decreaser?