How is torque produced by a force calculated?

The calculation of torque produced by a force takes into account both the magnitude of the force and its application point relative to the pivot, as well as the angle at which the force is applied. The correct formula for torque is given by Torque = Force × Distance × sin(θ), where "Distance" represents the distance from the pivot point to the line of action of the force, and θ is the angle between the force vector and the lever arm (the straight line from the pivot to where the force is applied).

The presence of the sine function is crucial because it adjusts the effective component of the force that contributes to producing rotation. When the angle is 90 degrees, sin(90°) equals 1, which maximizes the torque produced. Meanwhile, if the angle is 0 degrees or 180 degrees, the sine function yields zero, indicating no torque is produced since the force is applied along the line of action of the lever arm and does not induce rotation.

Other choices provided do not account for the angle or incorrectly define the relationship between torque, force, and distance, leading to misunderstandings about how rotational motion is generated. Understanding torque in this manner is essential for analyzing rotational systems effectively.