What is the formula for torque?

The formula for torque is represented as the product of the moment arm (the perpendicular distance from the axis of rotation to the line of action of the force), the force applied, and the sine of the angle (theta) between the force vector and the moment arm. This relationship is encapsulated in the equation:

Torque (τ) = Moment arm (r) * Force (F) * sin(theta).

This formula effectively captures how the angle of application influences the effectiveness of the force to create rotational motion. When the force is applied perpendicularly to the moment arm, the sine of 90 degrees is 1, resulting in maximum torque which occurs at this angle. Conversely, as the angle decreases, the effective component of the force contributing to torque diminishes, reducing the torque generated.

While other options touch on aspects related to rotational dynamics or linear motion, they do not express the complete relationship involved in calculating torque. For example, simply multiplying force by distance does not account for the angle at which the force is applied, which is crucial in determining the actual torque produced.