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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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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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Quote:
Original post by Jacob Roman
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 / 124.83161 = 7.85590 <---- correct amount of torque needed.

The other torque = 0.09807 / 124.83161 = 0.00079 <---- 1 pixel per second anyone? Too slow.

So your way seems wrong.


NO! Jacob, this is wrong!

You have mistakes here, my friend. You are not being rigorous at all, I'm afraid.

First, Jacob, what the hell are you doing???? You reported that 980 N-m was your torque. But now you've assigned Torque = 980/124---dividing a torque value by inertia gives you an angular acceleration. So, you're saying Torque = 7.86, which has units of angular acceleration. That is just fundamentally wrong. But, I believe this was just a typo. I believe you meant to write:


Angular Accel = 980.665 N-m / 124.83161 kg-cm2


...didn't you?

Now....there is another, SERIOUS problem here. A UNITS problem. You reported to me that 980.665 was Newton-meters. Your inertia values are kg-cm2. When you do 980/125, you're dividing Newton-meters by kg-cm2, a unit mismatch.

You gotta get it into your head to match your units up, dude! Either use 9.8 N-cm for torque, or convert that 125 into kg-m2 Do this and you will see that I am perfectly correct.

To help you out, 125 kg-cm2 works out to be 0.0125 kg-m2. You have to divide by 100 twice, since the cm are squared.

Now....if you take .098 N-m (the correct value) and divide by 0.0125, you get an angular acceleration of....7.84. ta da! Same answer, but this time with corrected units. correct units to the rescue!!!!



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Quote:
Original post by jjd
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.


No slip-up. 1kgf-cm == 9.8 N-cm. That centimeter is in the numerator not the denominator. Divide 9.8 N-cm by 100 to get rid of centimeters, then multiply by 1 to add back meters (same conversion you have listed) to get 0.098 N-m, as I originally reported.

Jacob had another units issue, which threw off his calc.

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I'm sure Roman made a mistake with his units, but you did say

Quote:

There is 1 meter per 100 cm. So the ratio of m/cm = 1/100.


and this is wrong. 100 cm = 1 m, so 100 = m / cm.

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For every 1 meter you can divide it into 100 centimeters (ie. 1m/100cm). So if you have 50cm, then you have 50cm * (1m/100cm) = .5m

The most important thing is that the units cancel. Doesnt make a difference if your talking 1 meter per 100 centimeters or .01 meters per 1 centimer.

--
Kory

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Quote:
Original post by jjd
I'm sure Roman made a mistake with his units, but you did say

Quote:

There is 1 meter per 100 cm. So the ratio of m/cm = 1/100.


and this is wrong. 100 cm = 1 m, so 100 = m / cm.


jjd, actually I agree that I've written something in error. Thank you for helping me to see that. The ratio of 1 m to 1 cm is 100 (as you wrote), not 1/100 (as I wrote).

But, it turns out, my conversions are still correct and yours and Jacob's are wrong. My error was simply in the way I wrote the symbology of those ratios.

Here's another way to read what you wrote: "The ratio of 1 meter to 1 centimeter is 100:1"

Here's the subtle bit. To do unit conversion (what we're trying to do here)...you must have a ratio of 1:1. You must multiply by a ratio that leads to a statement like the following:

"The ratio of x meters to y centimeters is 1:1", or

conversion ratio 1.0 = (x m) / (y cm)

So, the correctly-stated unit conversion ratio is 1 m / 100 cm, a value of 1/100, which reads "The ratio of 1 meter to 100 centimeters is 1:1"

Lets see why this works, while 100 = m/cm does not.

I have 1 centimeter. If I multiply by m/cm = 100, I get 100 meters. CLEARLY wrong. This is what you and Jacob did.

But, using my ratio, if I have 1 centimeter, and multiply by 1/100, I get .01 meters, which is exactly right.

Unfortunately, while the Internet is full of automatic unit converters, there is little information on how to properly derive conversions. But I will try to look for something that may make this a bit more obvious.

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Original post by grhodes_at_work
jjd, actually I agree that I've written something in error. Thank you for helping me to see that. The ratio of 1 m to 1 cm is 100 (as you wrote), not 1/100 (as I wrote).

But, it turns out, my conversions are still correct and yours and Jacob's are wrong.


You're welcome. I didn't go through any of Jacob's work, so I shouldn't have concluded that his answer was correct because of the coincidental factor involved.

I appreciate the effort you've gone to in your reply, however I did not say that the conversion factor should be 100*, just that 100 = m / cm, which it is. I hope others will benefit from the information you've provided.

[edit] *this is unclear, implicitly I was saying that this was the conversion factor in my first post, which is wrong as you pointed out. In my second post, my only point was that your original ratio was wrong, not that multiplying by 100 is the correct conversion.

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Quote:
Original post by grhodes_at_work
Quote:
Original post by Jacob Roman
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 / 124.83161 = 7.85590 <---- correct amount of torque needed.

The other torque = 0.09807 / 124.83161 = 0.00079 <---- 1 pixel per second anyone? Too slow.

So your way seems wrong.


NO! Jacob, this is wrong!

You have mistakes here, my friend. You are not being rigorous at all, I'm afraid.

First, Jacob, what the hell are you doing???? You reported that 980 N-m was your torque. But now you've assigned Torque = 980/124---dividing a torque value by inertia gives you an angular acceleration. So, you're saying Torque = 7.86, which has units of angular acceleration. That is just fundamentally wrong. But, I believe this was just a typo. I believe you meant to write:


Angular Accel = 980.665 N-m / 124.83161 kg-cm2


...didn't you?

Now....there is another, SERIOUS problem here. A UNITS problem. You reported to me that 980.665 was Newton-meters. Your inertia values are kg-cm2. When you do 980/125, you're dividing Newton-meters by kg-cm2, a unit mismatch.

You gotta get it into your head to match your units up, dude! Either use 9.8 N-cm for torque, or convert that 125 into kg-m2 Do this and you will see that I am perfectly correct.

To help you out, 125 kg-cm2 works out to be 0.0125 kg-m2. You have to divide by 100 twice, since the cm are squared.

Now....if you take .098 N-m (the correct value) and divide by 0.0125, you get an angular acceleration of....7.84. ta da! Same answer, but this time with corrected units. correct units to the rescue!!!!


I edited my post when I noticed I accidently put that angular acceleration formula in Torque while you typed this long one out, literally one minute after I posted it! Take a look. lol! ;)

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Original post by Jacob Roman
I edited my post when I noticed I accidently put that angular acceleration formula in Torque while you typed this long one out, literally one minute after I posted it! Take a look. lol! ;)


Heh hey; you're right, I missed your correction, :). Excellent!

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Quote:
Original post by jjd
I appreciate the effort you've gone to in your reply, however I did not say that the conversion factor should be 100*, just that 100 = m / cm, which it is. I hope others will benefit from the information you've provided.

[edit] *this is unclear, implicitly I was saying that this was the conversion factor in my first post, which is wrong as you pointed out. In my second post, my only point was that your original ratio was wrong, not that multiplying by 100 is the correct conversion.


Yes indeed. I do get a bit enthusiastic about all these fundamentals. I think the whole thread was a good exercise, and I hope it'll be useful to others down the road. Thank you for being involved.

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Quote:
Original post by grhodes_at_work
Quote:
Original post by Jacob Roman
I edited my post when I noticed I accidently put that angular acceleration formula in Torque while you typed this long one out, literally one minute after I posted it! Take a look. lol! ;)


Heh hey; you're right, I missed your correction, :). Excellent!


Now alls I gotta do is correct those damn units, and I got myself a killer DJ app going.

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