What is torque and how is it calculated?

01-What is torque?

Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear motion, torque is what causes an object to gain angular acceleration.

Torque is a vector quantity, and the direction of the torque vector depends on the direction of the force on the axis.

Anyone who has ever opened a door has an intuitive understanding of torque. When a person opens a door, they push the door on the side farthest from the hinges. Pushing on the side closest to the hinges requires a greater force. Although the work done is the same in both cases (a larger force is exerted over a smaller distance), people generally prefer to apply a smaller force, which is why door handles are usually located there.

02 Torque can be static or dynamic

Static torque is a type of torque that does not produce angular acceleration. A person pushing on a closed door is applying static torque to the door because, although a force is being applied, the door does not rotate about its hinges. A person pedaling a bicycle at a constant speed is also applying static torque because they are not accelerating. The drive shaft in a race car accelerating from the starting line carries dynamic torque, because it must produce angular acceleration of the wheels while the race car accelerates along the track. The terminology used to describe torque can be confusing. Engineers sometimes use "moment" or "torsion" interchangeably with "torque." The radius through which the force acts is sometimes called the moment arm.

03 How to calculate torque — the magnitude of the torque vector

The torque produced by a given force is τ = F ⋅ r ⋅ sin(θ), where r is the length of the moment arm and θ is the angle between the force vector and the moment arm. For the door shown in Figure 1, the force is applied at a right angle (90°) to the moment arm, so the sine term equals 1 and τ = F ⋅ r. By convention, the direction of the torque vector can be found using the right-hand grip rule. If the hand is curled along the axis of rotation and the fingers point in the direction of the force, the torque vector points in the direction of the thumb, as shown in Figure 2.
*Figure 2: Direction of the torque vector found using the right-hand rule*

04 How to measure torque?

The unit of torque is the Newton-meter (N·m). In metric units, kilogram-force is commonly used. This can be confusing because, in everyday language, kilogram-force is sometimes used as a unit of mass and sometimes as a unit of force. Here it means kilogram-force, which is the force exerted by Earth's gravity on a one-kilogram object. These units are generally related as 1 kilogram-force ≈ 9.8 Newton-meters (N·m). Measuring static torque in a non-rotating system is usually easy and can be done by measuring force. Given the length of the moment arm, the torque can be found directly. Measuring torque in a rotating system is much more difficult. One method works by measuring the strain within the metal of a drive shaft that is transmitting torque and wirelessly transmitting this information.