For torque due to a force F applied at radius r with angle theta between r and F, which expression is correct?

• A. tau = r F cos theta
• B. tau = F
• C. tau = r F sin theta
• D. tau = r F

Answer: (C)

Torque measures how strongly a force tends to rotate an object about a pivot. The rotational effect depends on how far from the pivot the force is applied (the lever arm, r) and how much of the force acts perpendicular to that lever arm. The torque magnitude is given by the cross product, |τ| = |r × F| = r F sin(theta), where theta is the angle between r and F. The perpendicular component of the force is F sin(theta), and multiplying by the lever arm r gives the rotational tendency: r F sin theta. This is why the expression with sin theta is the correct one. When theta is 90°, you get the maximum torque rF; when theta is 0°, the torque is zero. The direction of torque is perpendicular to the plane formed by r and F, determined by the right-hand rule.