Enter the total force, radius of the applied force, and the angle at which it is applied to calculate the total torque on an object.

## Toque Formula

Torque is a force that is applied along a radius that causes and object to rotate. Force, just like velocity is a vector quantity meaning it has a magnitude and direction. With that said, the direction of the torque is often ignored in some calculations, especially in your introductory physics classes.

Torque can be calculated through the following formula:

(t) = (r) * (F) * sin (theta)

- Where t is torque in
- r is radius
- F is force
- and theta is the angle between

This can also be written as a cross product of two vectors, but we will not go that deep in this article as it’s a little more advanced and harder to write out. Torque causes an object to rotate and as a result, it will make this object accelerate in an angular motion, and give it momentum. This will cause the object to have a velocity after some period of time, and in tern will have a kinetic energy. This can be calculated through the following equation:

Energy = torque * theta

Where theta is the total angle rotated by that object.

## How to Calculate Torque

Let’s take a look at an example of how to calculate torque in a real world sending. Let’s assume we are looking at car. In that car there is a motor which applied a force to a gear. That gear is at some radius which is then attached to an axle.

- First, we must calculate the total force produced by the engine. This is usually given as a specification on a car, but for our example we will assume a force of 3000N.
- Next, we must determine the radius of the gear. This can be done simply through hand measuring it. For our example we will assume a radius of .25m
- Next, we need to determine the angle at which that gear applies force to the axle. In this case the force is always applied at a 90 degree angle, and the sin of 90 = 1, so it simplifies the equation.
- Finally, enter all of the information into the equation or calculator above. T = 3000N * .25 * 1 = 750 N*m of torque. Not bad for a small car!

These types of torque problems become increasingly more difficult if the force is not applied at a 90 degree angle, and there are other forces involved. For instance, in the example above, there is actually friction acting against the movement of the gear and axle, therefore the net torque the car can output will actually be less that what we calculated above.

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