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

In summary, the equation for the torque is: Tcom = I / (I + m * (r * r)) * T. The equation for the force due to torque is: Fcom = r x T.
  • #1
log0
35
0
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 ?
 
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  • #2
Welcome to PF!

Hi log0! Welcome to PF! :wink:
log0 said:
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. :smile:
 
  • #3
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:
  • #4
log0 said:
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 :wink:)

Yes, that's right …

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). :smile:
 
  • #5
OK, Thanks tiny-tim. :smile:
 

1. What is torque applied at offset?

Torque applied at offset refers to the rotational force that is applied at a distance from the axis of rotation.

2. How is torque applied at offset calculated?

To calculate torque applied at offset, you need to multiply the force applied by the distance from the axis of rotation. The formula is: Torque = Force x Distance.

3. What is the difference between torque and torque applied at offset?

Torque is a measure of rotational force, while torque applied at offset takes into account the distance from the axis of rotation. This means that torque applied at offset is a more accurate measure of the rotational force in a system.

4. Why is torque applied at offset important?

Torque applied at offset is important because it allows us to understand and predict the rotational motion of objects. It is also essential in engineering and design, as it helps determine the strength and stability of structures.

5. How does torque applied at offset affect rotational motion?

Torque applied at offset affects rotational motion by causing an object to rotate around its axis. The larger the torque applied at offset, the faster the rotational motion will be. It also determines the direction of rotation, as torque applied at offset can be either clockwise or counterclockwise.

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