What equation represents the torque in a mechanical system?

Torque in a mechanical system is defined as the rotational equivalent of linear force. The formula for torque (T) is given by the product of the distance (r) from the pivot point to the point of force application, the magnitude of the force (F), and the sine of the angle (theta) between the force vector and the lever arm.

This relationship illustrates that only the component of the force that acts perpendicular to the lever arm contributes to the torque. The sine function accounts for this, ensuring that if the angle is 0 degrees (force is applied along the line of the lever arm), the torque is zero, as there is no effective moment causing rotation. Conversely, when the angle is 90 degrees, sine equals one, indicating maximal torque.

The other options do not accurately represent the concept of torque within a mechanical system according to this definition. The presence of cosine or tangent in formulas does not relate to how torque is derived but instead reflects other relationships in physics that do not apply to torque production specifically.