How do you calculate the torque produced by a force applied at a distance from the pivot?

How do you calculate the torque produced by a force applied at a distance from the pivot?

• A. Torque equals force times area.
• B. Torque = Force × perpendicular distance from the pivot (T = F × d).
• C. Torque equals force divided by distance.
• D. Torque equals force times velocity.

Answer: (B)

Torque is the rotational effect of a force about a pivot. It depends on how hard you push and how far from the pivot you push—the lever arm. The lever arm is the perpendicular distance from the pivot to the line of action of the force. Multiply the force by that perpendicular distance: τ = F × d. If the force isn’t perpendicular, you multiply by the sine of the angle between the force and the lever arm, giving τ = F d sin(θ). When the force is perpendicular, sin(90°) = 1, so it reduces to τ = F d. If the force passes through the pivot, the lever arm is zero and there is no torque. The option that uses area isn’t related to rotational tendency here, dividing by distance would misrepresent how lever arms work, and multiplying by velocity confuses torque with other quantities. For a perpendicular force, torque equals force times the distance from the pivot; for angled forces, use the sine factor to get the effective lever arm. Example: a 10 N force 0.5 m away produces 5 N·m of torque when perpendicular.

Torque is the rotational effect of a force about a pivot. It depends on how hard you push and how far from the pivot you push—the lever arm. The lever arm is the perpendicular distance from the pivot to the line of action of the force. Multiply the force by that perpendicular distance: τ = F × d. If the force isn’t perpendicular, you multiply by the sine of the angle between the force and the lever arm, giving τ = F d sin(θ). When the force is perpendicular, sin(90°) = 1, so it reduces to τ = F d. If the force passes through the pivot, the lever arm is zero and there is no torque. The option that uses area isn’t related to rotational tendency here, dividing by distance would misrepresent how lever arms work, and multiplying by velocity confuses torque with other quantities. For a perpendicular force, torque equals force times the distance from the pivot; for angled forces, use the sine factor to get the effective lever arm. Example: a 10 N force 0.5 m away produces 5 N·m of torque when perpendicular.