Torque can be simply defined as the tendency of a force to create a rotation. Let’s dig in and find out more.
By the end of this topic, you are expected to:
Torque is also known as the turning effect, the moment of force or moment. It refers to the rotational equivalent of linear force. This concept came with the studies by Archimedes of the usage of levers. Just like a linear force is a pull or a push, a torque can be said to be the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. Torque is represented by the symbol Ƭ (the lowercase Greek letter tau). When torque is referred to as moment, it is commonly denoted by M.
Ƭ = r x F
L = r x p
In 3D, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector and the force vector. The magnitude of torque of a rigid body is dependent on three quantities: the applied force, the lever arm vector that connects the origin to the point of application of force, and the angle between the force and the lever arm vectors. In symbols:
Ƭ = r x F
Ƭ = ‖r‖ ‖F‖ sin θ where,
Ƭ is the torque vector and Ƭ is the magnitude of the torque.
r is the position vector (a vector from the origin of the coordinate system that is defined to the point where the force is applied)
F is the force vector
X denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule, θ is the angle between the lever arm vector and the force vector.
The SI unit for torque is N.m.
A force applied at a right angle to a lever multiplied by its distance from the fulcrum of the lever is its torque. A force of three newtons applied 2 meters from the fulcrum, for instance, exerts the same torque as a force of one newton that is applied 6 meters from the fulcrum. The direction of the torque is determined by using the right-hand grip rule: if fingers of the right hand are curled from the direction of the lever arm to the force’s direction, the thumb points in the direction of the torque.
Generally, the torque on a point particle can be said to be the cross product. Ƭ = r x F where,
r is the position vector of the particle relative to the fulcrum, and F is the force that acts on the particle.
