leverarm

LeverArm, in physics and biomechanics, refers to the perpendicular distance from a pivot point or axis to the line of action of a force. It is also known as the moment arm. The lever arm determines the torque produced about the pivot.

The torque produced by a force is given by the cross product τ = r × F, where r is the position vector from the pivot to the point of force application and F is the force vector. The magnitude of the lever arm is r⊥ = r sinθ, with θ the angle between r and F. Therefore, τ = F r sinθ. If the force is applied perpendicular to the lever arm (θ = 90°), the torque is maximized (τ = F r). If the force is parallel to the lever arm (θ = 0° or 180°), the lever arm is zero and no torque is generated.

Units are consistent with torque in newton-meters (N·m), derived from force in newtons and distance in meters. The direction of torque is determined by the right-hand rule: curling from r to F, the thumb indicates the torque axis.

Examples illustrate the concept. Pushing a door near the handle creates a larger lever arm than pushing near the hinge, producing greater torque for the same applied force. In biomechanics, a muscle’s lever arm—the distance from a joint center to the muscle’s line of action—varies with joint angle, influencing the torque the muscle can generate. In engineering, lever arms are central to lever systems and mechanical advantage, affecting required force and efficiency.

See also: torque, lever (mechanics), moment arm, biomechanics.