Torque produced by a horizontal lever arm of length l with a perpendicular force F is equal to which expression?

• A. tau = F / l
• B. tau = F
• C. tau = l^2
• D. tau = l * F

Answer: (D)

Torque about a pivot is the rotational effect of a force and is given by tau = r F sin theta, where r is the distance from the pivot to where the force is applied and theta is the angle between the force and the lever arm. If the force is perpendicular to the lever arm, theta = 90°, so sin theta = 1 and tau = r F. With a lever arm of length l, that becomes tau = l F. This matches the idea that both a longer arm and a stronger perpendicular force increase the twisting effect. The other expressions don’t fit because they miss either the distance, the angle dependence, or give incorrect units (for example, F/l has units of force per length, and l^2 has units of length squared).