How can I calculate torque and force on a rigid body with an offset axis?

[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 ?

 

[tiny-tim]

Welcome to PF!

Hi log0! Welcome to PF!

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?

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. ​

 

[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?

 

[tiny-tim]

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

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

Yes, that's right …

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

 

[log0]

OK, Thanks tiny-tim.