In the torque formula, what must be true about the force and distance applied?

In the context of torque, the relationship between force, distance, and the angle at which the force is applied is fundamental. Torque is calculated using the formula τ = r × F × sin(θ), where τ is the torque, r is the distance from the pivot point to where the force is applied, F is the magnitude of the force, and θ is the angle between the force vector and the lever arm.

For maximum torque to be generated, the force must be applied perpendicularly to the lever arm (where θ equals 90 degrees). When the force is perpendicular to the lever arm, the sine of the angle is at its maximum value of 1, which maximizes the torque produced. If the force is not perpendicular, the effective distance that contributes to the torque decreases, reducing the value of torque.

Thus, for the torque to be effectively calculated and maximized, the force must be applied at a right angle (90 degrees) to the line drawn from the pivot point to the point of force application. This principle is why the correct answer emphasizes the necessity of perpendicularity between the force applied and the distance from the pivot point.