The torque for lever arm length l and force F is given by which expression?

The torque for lever arm length l and force F is given by which expression?

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

Answer: (C)

Torque measures how strongly a force tends to rotate something, and it depends on both how far from the pivot you push (the lever arm) and how the force is oriented relative to that lever arm. The general expression is tau = r F sin(theta), where r is the lever arm length and theta is the angle between the lever arm and the force. If the force is perpendicular to the lever arm, theta = 90°, so sin(theta) = 1 and tau = r F. With the lever arm length labeled as l, that becomes tau = l F. So the correct expression is the one where torque equals the lever arm length times the force, tau = l F. The other forms miss the distance, or include an extra factor, or give a reciprocal dependence that doesn’t match how torque depends on the geometry. The direction of tau is perpendicular to the plane, determined by the right-hand rule.

Torque measures how strongly a force tends to rotate something, and it depends on both how far from the pivot you push (the lever arm) and how the force is oriented relative to that lever arm. The general expression is tau = r F sin(theta), where r is the lever arm length and theta is the angle between the lever arm and the force.

If the force is perpendicular to the lever arm, theta = 90°, so sin(theta) = 1 and tau = r F. With the lever arm length labeled as l, that becomes tau = l F.

So the correct expression is the one where torque equals the lever arm length times the force, tau = l F. The other forms miss the distance, or include an extra factor, or give a reciprocal dependence that doesn’t match how torque depends on the geometry. The direction of tau is perpendicular to the plane, determined by the right-hand rule.