The force applied to a lever multiplied by its distance from the lever's fulcrum, the length of the lever arm, is its torque. A force of three newtons applied two meters from the fulcrum, for example, exerts the same torque as one newton applied six meters from the fulcrum. This assumes the force is in a direction at right angles to the straight lever. The direction of the torque can be determined by using the right hand grip rule: curl the fingers of your right hand the direction of rotation and stick your thumb out so it is aligned with the axis of rotation. Your thumb points in the direction of the torque vector.
Mathematically, the torque on a particle (which has the position r in some reference frame) can be defined as the cross product:
where
r is the particle's position vector relative to the fulcrum
F is the force acting on the particle.
The torque on a body determines the rate of change of its angular momentum,
r is the particle's position vector relative to the fulcrum
F is the force acting on the particle.
The torque on a body determines the rate of change of its angular momentum,
where
L is the angular momentum vector
t stands for time.
As can be seen from either of these relationships, torque is a vector, which points along the axis of the rotation it would tend to cause.
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