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Jacob Roman

Applied Torque [RESOLVED]

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I'm trying to pull off applied torque correctly, but at first, I thought I can just use some torque value, but I had to multiply it by the objects inertia to get the correct results I'm looking for, but unfortunately it cancelled out the inertia in the angular acceleration: //Located in some function Torque.Net = 9.8 * Obj.Inertia //Done before integration Angular_Acceleration = Torque.Net / Obj.Inertia Basically, what I'm doing is spinning a vinyl on a turntable with the mouse, with friction slowing it down. Was I suppose to multiply the torque by the inertia in my case of applied torque, or what? [Edited by - Jacob Roman on June 16, 2006 5:30:10 AM]

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Well, torque equals the inertia times the angular acceleration. So, if you have the inertia and the known, exact angular acceleration, you can compute torque by multiplying inertia times angular acceleration. (Normally, you know torque and inertia, but do not know the acceleration.)

But, in your case, based on prior threads here, I do not believe this is the case. I think you are telling us that 9.8 is the torque that you would like to apply. Is this interpretation correct? Notice that ultimately you are really just specifying that Angular_Acceleration = 9.8, but with a couple of extra unnecessary calculations. What are the units that you have for this torque?

My question back to you is....when you write "but I had to multiply it by the objects inertia to get the correct results I'm looking for"....what do you mean by "correct results"? Just based on your visual observation?

Jacob, you've been working on this for a while, and so I believe you do want to understand the correct math and physics. I hope I have contributed helpful info in your past threads, and that I can contribute something useful in this one as well.

So, my first lesson is that you must pay attention to the units in the equations you are solving. The units can tell you a hell of a lot about whether an equation is correct or incorrect. If the units aren't the same for every term in an equation, the equation is broken!!! It might be broken even if the units are correct, but if the units aren't balanced, it is absolutely wrong. Unit balancing is a necessary, but insufficient condition. Lets look at some preliminaries:

units of torque = force times length. Ex: Newton-meters, foot-pounds.

But force itself is mass * length / time2

So torque is also mass * length2/time2. Shorthand: "m*l*l/(t*t)"

units of angular acceleration = 1/time2. Ex: 1/second2. This is really radians/second2, but for the purpose of units analysis/balancing you treat radians as nil. Shorthand: "1/(t*t)"

units of moment of inertia = mass * length-squared. Ex: Kilogram-meter2. Shorthand: "m*l*l"

So, lets look at the basic equation discussed above:

Torque = Inertia * Angular Acceleration

Rewrite as units, using the shorthand notation:


m*l*l 1
----- = (m*l*l) * -----
t*t t*t


Simplify the right side using algebra---just multiply through, and you will see that they are identical. The units of the left side are equal to the units of the right side. This relationship is consistent in terms of units.

On the other hand, lets do what you did....multiply torque by inertia. I am assuming that 9.8 was indeed in correct units for torque:

Torque * inertia units are:


m*l*l m2*l4
----- * m*l*l = -----
t*t t*t


The simplified units for your extra multiply give you completely bogus units...so when you multiplied by angular acceleration, you created a meaningless value.

See if that makes sense. Look at your actual units for the value 9.8 you listed, and go through this same units-analysis exercise. See if you can find or confirm where your equations are going wrong.

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Quote:
Original post by Jacob Roman
//Located in some function
Torque.Net = 9.8 * Obj.Inertia


I dont think this bit makes a whole lot of sense, so I would start with figuring out why you needed to add it and work from there.

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9.8 was my torque cause 1 kgf-cm is 9.8 newtons, but multiplying it by its inertia didn't make sense to me either, hence thats why I made this thread.

Perhaps there is a problem in my prog that involved the units. I'm gonna double check to be sure though. And the "correct results" wasn't just correct visually, but numerically as well. Hell, I practically got it rotating at exactly 33.33333 RPM in real time.

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Quote:
Original post by Jacob Roman
9.8 was my torque cause 1 kgf-cm is 9.8 newtons


What you say here is actually wrong. kgf is a force. Newtons are a force. kgf-cm is a torque. 1 kgf-cm cannot be equal to 9.8 Newton's since a torque cannot be equal to a force. You have a units problem right in this statement!

So, this little units problem is easy to correct. 1 kgf does == 9.8 Newton's (force == force). And it is valid to say that 1 kgf-cm is == 9.8 Newton-cm (torque == torque). or 1 kgf-m == 9.8 Newton-m. But 1 kgf-cm != 9.8 Newton-m (different length units on each side). In this case, 1 kgf-cm == 0.098 Newton-m (since there are 100 cm in 1 m). That length unit can make all the difference in the world.

When doing physics, one should pay rigorous attention to detail. You just gotta make sure you have the same units for all values that are compared directly. I hope this helps you find the key to the mixup!

[Edited by - grhodes_at_work on June 14, 2006 1:06:40 PM]

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Actually it was 980 N-m not 0.098 N-m. And believe it or not, it works! All of my physics math is now correct! Thanks! Now I just gotta add sound so I can have scratching capabilities (got source code for that) and I'm all set.

[Edited by - Jacob Roman on June 14, 2006 5:33:20 PM]

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Quote:
Original post by Jacob Roman
Actually it was 980 N-m not 0.098 N-m. And believe it or not, it works! All of my physics math is now correct! Thanks! Now I just gotta add sound so I can have scratching capabilities (got source code for that) and I'm all set.


Something else in the units doesn't add up. 1kgf-cm maps to 9.8 N-cm. There is 1 meter per 100 cm. So the ratio of m/cm = 1/100. Multiply 9.8 N-cm * 1 m/100 cm to get 0.098 N-m as I reported (the cm cancels algebraically).

Have you seen Guitar Hero? Great game. Kind of like a dancing/rhythm game, but for guitar player rocker wannabees. Hmmm. I'm imaging your game is maybe similar, but for DJ's?

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Well it's time I prove it to you.

Vinyl Mass = 0.14969 kg
Vinyl Radius = 14.60500 cm
Vinyl Inertia = 0.5 * Mass * Radius ^ 2 = 15.96441

Platter Mass = 0.74072 kg
Platter Radius = 17.14500 cm
Platter Inertia = 0.5 * Mass * Radius ^ 2 = 108.8672

Object Inertia = Vinyl Inertia + Platter Inertia = 124.83161

Torque = 980.665

Angular acceleration = 980.665 / 124.83161 = 7.85590 <---- correct amount of torque needed.

The other torque = 0.09807

Angular acceleration = 0.09807 / 124.83161 = 0.00079 <---- 1 pixel per second anyone? Too slow.

So your way seems wrong.

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980.665 is correct because m/cm should be 1.0 / (1.0 x 10-2) = 100.0

Grahams reasoning is correct, he's just made a little slip up by the looks of things.

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