Applied Torque [RESOLVED]

Math and Physics Programming

Started by Jacob Roman June 13, 2006 02:22 PM

18 comments, last by Jacob Roman 17 years, 10 months ago

1,385

June 15, 2006 12:28 PM

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!!!!

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

grhodes_at_work

1,385

June 15, 2006 12:34 PM

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.

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

jjd

2,140

June 15, 2006 12:37 PM

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.

--www.physicaluncertainty.com
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kspansel

122

June 15, 2006 01:04 PM

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

"The pioneers of a warless world are the youth who refuse military service" - Albert Einstein

grhodes_at_work

1,385

June 15, 2006 01:06 PM

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.

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

jjd

2,140

June 15, 2006 01:38 PM

Quote: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.

--www.physicaluncertainty.com
--linkedin
--irc.freenode.net#gdnet

Jacob Roman

120

Author

June 15, 2006 02:17 PM

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! ;)

grhodes_at_work

1,385

June 15, 2006 02:50 PM

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!

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

grhodes_at_work

1,385

June 15, 2006 02:53 PM

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.

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

Jacob Roman

120

Author

June 16, 2006 05:29 AM

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.

Applied Torque [RESOLVED]

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