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**New Theories / What's the unit of Torque?**

« **on:**09/08/2024 03:27:10 »

This is a spin-off of my other thread. I thought the discussion would be short and would quickly come into conclusion, but it seems I was not the case. Let's discuss into more details here.

I asked Gemini for other Physical Measures with the Same UnitsI told Gemini that energy is torque times the angle of rotation.QuoteExcellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:

...

2. Torque and Energy

* Both measured in newton-meters (Nm) or joules (J).

* Torque is a rotational force, while energy is the capacity to do work.

...

While the other points are basically pairs of the same measures, the second point tells a different story. There is something missing here.QuoteYou're absolutely right!It means that the proper unit for torque is Joule/radian, or Newton meter/radian.

Energy = Torque x Angle of Rotation

This equation is a fundamental relationship in rotational mechanics. Here's a breakdown:

* Torque: A measure of the force that can cause an object to rotate around an axis. It's analogous to force in linear motion.

* Angle of rotation: The amount of rotation an object undergoes around an axis.

When you multiply torque by the angle of rotation, you get the work done, which is a form of energy.

Key points:

* This equation holds true for constant torque. If the torque varies, integration is required.

* The units of torque (Newton-meter) multiplied by the unit of angle (radians) give the unit of energy (joules).

I found many people being confused about measurement units involving radian, which is often omitted for being a dimensionless quantity.

The unit radian for measuring angle of rotation is convenient since the traveling distance of a point due to 1 radian rotation equals the radius of rotation.Quotehttps://en.wikipedia.org/wiki/Radian

An arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.