### Author Topic: Equivalent mass of rotating parts  (Read 990 times)

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#### nForce

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##### Equivalent mass of rotating parts
« on: November 10, 2019, 02:23:47 pm »
Hello,

I want to calculate the extra mass of a vehicle when the vehicle is moving. We add this extra mass to the mass of the vehicle it's due to rotating parts. When searching on the web I found this: https://www.physicsforums.com/threads/equivalent-mass-of-rotating-parts.936039/

I don't understand which equation is here relevant. I would like to know the equation for mass_equ.
Thanks for the help.

#### m98

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##### Re: Equivalent mass of rotating parts
« Reply #1 on: November 10, 2019, 03:24:16 pm »
What are you even trying to accomplish? A vehicle certainly gains no mass by accelerating, except dead insects, maybe.

#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #2 on: November 10, 2019, 04:39:30 pm »
What are you even trying to accomplish? A vehicle certainly gains no mass by accelerating, except dead insects, maybe.

No, you don't understand. This extra mass is virtual. We have the mass of the car + virtual mass when speeding up. The virtual mass is the equivalent mass of rotating parts.

#### T3sl4co1l

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##### Re: Equivalent mass of rotating parts
« Reply #3 on: November 10, 2019, 05:03:37 pm »
m98 -- the problem is analogous to the physics riddle of: "how long does it take for a ball to fall down an incline with friction coefficient a. zero (frictionless), and b. 1.0?"

In the first case, the ball does not rotate, and the answer is simply the physics of a mass on an incline.  In the second, the ball rotates; its inertia is coupled to its mass by friction, and the answer is (for a uniform ball I think) 40% more or something like that.

The mass equivalent of rotating parts is not very much in a typical vehicle, though, so I don't know to what end the OP needs this.

Also, regarding the link, I'll note that the transmission was omitted, and the engine and transmission are complicated by shifting anyway.  Better to ignore them both; they are turned into heat dissipated during shifting (equivalent to switching loss in an electrical circuit).

Both would need to be included, in a dynamics problem where the transmission is locked in a given gear and the vehicle is accelerated some way.

In any case, that's simply how it's calculated, it's straightforward.  You get the moment of inertia, link it to mass via gear and wheel ratios, and there you are.  Just ratios and addition.  You need to know the moment somehow or another, which if you know the geometry of the elements, it can be calculated roughly; else it can be measured, or perhaps looked up in a catalog/datasheet.

On a more fanciful note, there is real mass gain, on the order of micrograms, due to the energy stored in the rotating masses and Special Relativity.  There is also a frame-dragging effect of those masses on nearby space (General Relativity).  Both are essentially impossible to measure when materials lighter than neutronium are involved.

Tim
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#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #4 on: November 10, 2019, 05:43:21 pm »
So this is the formula for force, which is pointed backward like friction, air drag? So if I want to get the equivalent mass, I need the acceleration of the car for a particular moment on the road?

#### StillTrying

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##### Re: Equivalent mass of rotating parts
« Reply #5 on: November 10, 2019, 06:24:56 pm »
After reading the thread 3 times, I'm still
CML+  That took much longer than I thought it would.

#### soldar

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##### Re: Equivalent mass of rotating parts
« Reply #6 on: November 10, 2019, 07:53:50 pm »
After reading the thread 3 times, I'm still

I think I understand the question. Suppose you have a bicycle with a box carrying a load of 100 Kg. When you accelerate forward you need to do provide energy in order to accelerate that 100 Kg forward.

Now suppose the 100 KG, instead of being on the carrier is distributed on the rim of the wheels. Now you have to provide the same energy to accelerate that mass forward but additionally you need to provide energy to get that mass spinning.

The OP is, like many, poorly explained but I think this is the question.
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#### SiliconWizard

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##### Re: Equivalent mass of rotating parts
« Reply #7 on: November 10, 2019, 08:42:52 pm »

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#### soldar

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##### Re: Equivalent mass of rotating parts
« Reply #8 on: November 10, 2019, 09:28:46 pm »
All my posts are made with 100% recycled electrons and bare traces of grey matter.

#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #9 on: November 11, 2019, 06:11:08 am »
So this is the formula for force, which is pointed backward like friction, air drag? So if I want to get the equivalent mass, I need the acceleration of the car for a particular moment on the road?

Can someone just answer my question? Because I want to understand.

#### T3sl4co1l

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##### Re: Equivalent mass of rotating parts
« Reply #10 on: November 11, 2019, 06:16:14 am »
Force is F = m*a, or for a known moment of inertia, F = I*a/r.

Tim
Seven Transistor Labs, LLC
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#### soldar

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##### Re: Equivalent mass of rotating parts
« Reply #11 on: November 11, 2019, 07:00:58 am »
Can someone just answer my question? Because I want to understand.

The way you put your question shows you want a very simple answer to a rather complicated question. You have been provided with a link to a page that answers the question. If that answer is too complex for you then I can give you a simpler answer: 42.

42 is always the answer to everything in a simpler universe.
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#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #12 on: November 11, 2019, 06:21:47 pm »
Can someone just answer my question? Because I want to understand.

The way you put your question shows you want a very simple answer to a rather complicated question. You have been provided with a link to a page that answers the question. If that answer is too complex for you then I can give you a simpler answer: 42.

42 is always the answer to everything in a simpler universe.

So according to the website the additional mass is I*((w/v)^2)? Where w = angular velocity and v = linear velocity of a vehicle. I just have to get the rotational inertia of the wheel. Do I now understand correctly?

#### soldar

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##### Re: Equivalent mass of rotating parts
« Reply #13 on: November 11, 2019, 06:29:21 pm »
So according to the website the additional mass is I*((w/v)^2)? Where w = angular velocity and v = linear velocity of a vehicle. I just have to get the rotational inertia of the wheel. Do I now understand correctly?

I don't know. I am not going to study that page in detail. I thought you were going to do that and explain it to the rest of us.

In any case, the wheels are probably not the biggest part of rotational inertia. Probably the crankshaft, flywheel and other parts rotating fast add more but I don't know for sure.

You can study that page in detail if you want to know the exact answer.
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#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #14 on: November 11, 2019, 06:45:03 pm »
Maybe Tim knows.

#### T3sl4co1l

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##### Re: Equivalent mass of rotating parts
« Reply #15 on: November 11, 2019, 07:34:40 pm »
Force is F = m*a, or for a known moment of inertia, F = I*a/r.

It does not depend on velocity squared, that would be energy at best.  Dimensional analysis is your friend!

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!

#### SiliconWizard

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##### Re: Equivalent mass of rotating parts
« Reply #16 on: November 11, 2019, 07:37:30 pm »
Regarding rotating wheels, you can check this out:
https://www.wolframalpha.com/widgets/view.jsp?id=2d14c4d40d3f9efdc9b810336eab3ca7
(disclaimer: I didn't check that what it computes was correct, just played with it a little.)

It gives you the equivalent mass for a 2-wheel system on an axle (obviously simplified model!)

Check with typical values for car wheels/axles, you'll get to see that the equivalent mass is definitely not negligible. (Again disclaimer: I can't certify it gives correct values.)

#### nForce

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##### Re: Equivalent mass of rotating parts
« Reply #17 on: November 12, 2019, 07:30:59 am »
Force is F = m*a, or for a known moment of inertia, F = I*a/r.

It does not depend on velocity squared, that would be energy at best.  Dimensional analysis is your friend!

Tim

But how? Can you look the website. There is a formula with angular velocity and linear velocity.

Smf