When calculating the torque, what angle does the force and the arm of force need to make?

When calculating torque, the most effective angle for the application of force in relation to the lever arm is 90 degrees. At this angle, the force is maximally effective in producing rotation around the pivot point, as all of the force contributes to the torque and none of it is wasted in counteracting or being ineffective.

Torque is defined mathematically as the product of the force applied and the distance from the pivot point (lever arm) to where the force is applied, with the sine of the angle between the force vector and the lever arm incorporated into the calculation. When this angle is 90 degrees, the sine value is 1, maximizing the torque.

For angles less than or greater than 90 degrees, the sine function yields lower values, meaning that not all of the applied force contributes to the torque. Therefore, the angle of 90 degrees is optimal for ensuring that the full force applied is utilized in generating torque.