Using torque about one point to get torque about a different point

[rachaelvicto]

Hello All,
I'm not a physicist so this may be very straightforward, I'm just not seeing it. If anyone can help it would be greatly appreciated.

What I would like to do is take an equation for torque for an object about one point and use this result to get the torque for the same object about a different point. I am trying to calculate the forces and torque for an L shaped dielectric in a gaussian profile beam using ray optics. As I increase the length of the lower leg on the L, I want to see how this affects the torque balance. If I calculate the torque about the focal point, viola, nice clean answer. It is much easier to think about the problem physically for torques calculated about the center of mass for the dielectric. The actual calculation of the torque about the center of mass is, however, kind of obscenely complicated.

Any ideas?
Thanks guys.

 

[eljose79]

Hi there! As a physicist, I can definitely help you with your problem. Calculating torque about different points can be a bit tricky, but it can be done. One way to approach this problem is to use the parallel axis theorem, which states that the moment of inertia of an object about a point is equal to the moment of inertia about its center of mass plus the mass of the object times the square of the distance between the two points.

In your case, if you are calculating the torque about the focal point, you can use this theorem to find the moment of inertia about the center of mass and then add the appropriate term for the distance between the two points. This will give you the torque about the center of mass. Alternatively, you can use the perpendicular axis theorem, which states that the moment of inertia about an axis perpendicular to the plane of the object is equal to the sum of the moments of inertia about two perpendicular axes in the plane of the object. This can also be useful in your calculation.

In terms of simplifying the calculation of torque about the center of mass, you can break down the object into smaller, simpler shapes and calculate the torque for each shape separately. Then, you can use the parallel axis theorem to combine the torques and find the total torque about the center of mass. This approach can make the calculation more manageable and less complicated.

I hope this helps and good luck with your research! Don't hesitate to reach out if you have any further questions.