Torque applied at offset

1. Apr 13, 2010

log0

Hi, I am a noob to physics trying to get a better understanding of rigid bodies.

How do I calculate the torque, force at the center of mass of a rigid body given a torque whose axis is not going through the center of mass of the body?

Example(engine axis doesn't go trough com):
[URL]http://www.piercy.co.za/images/seawind3views1.jpg[/URL]

I found the following equation for the torque:
Tcom = I / (I + m * (r * r)) * T

I is the scalar inertia relative to torque axis n:
n = T / |T|
I = (Inertia * n) * n

I looks like the parallel axis theorem is used here. Is it correct?

And how do I calculate the force due to torque:
Fcom = r x T ?

Last edited by a moderator: Apr 25, 2017
2. Apr 13, 2010

tiny-tim

Welcome to PF!

Hi log0! Welcome to PF!
If by "torque" you mean a pure moment (a couple ), then (unlike a force) it has no point of application.

It's the same about any point.

3. Apr 13, 2010

log0

You mean the reaction torque that rotates the fuselage of the aircraft around its center of mass doesn't depend on the placement of the engine (is opposite to the engine torque)?

I tried a derivation using a force couple:
F0 = -F1
T = r0 x F0 + r1 x F1

Tcom = (r + r0) x F0 + (r + r1) x F1 = r0 x F0 + r1 x F1 + r x (F0 + F1) = T
Fcom = F0 + F1 = 0

Right?

Last edited: Apr 13, 2010
4. Apr 13, 2010

tiny-tim

(try using the X2 tag just above the Reply box )

Yes, that's right â€¦

when you change the "centre" by a displacement r, you add r x Fnet to the moment, and Fnet is zero for a couple (a pure moment).

5. Apr 13, 2010

log0

OK, Thanks tiny-tim.