If the force applied is not perpendicular to the radius, how can torque be calculated?

Torque, which is essentially a measure of how effectively a force can cause an object to rotate about a pivot point, depends on two key factors: the magnitude of the force applied and the distance from the pivot point (the radius) at which this force is applied. When the force is applied at an angle to the radius, it is crucial to find the component of the force that acts perpendicular to the radius since only this component contributes to the torque.

To find the torque when the force is not applied perpendicular to the radius, the correct approach is to calculate the perpendicular component of the force. This is where trigonometry comes into play, particularly the SOHCAHTOA relationships. By identifying the angle between the force vector and the radius, one can use trigonometric functions to express the perpendicular component.

Using sine, for instance, we consider the angle between the force and the line from the pivot point to the point of force application. The formula to determine the torque (τ) in this case is τ = r × F ⊥, where F ⊥ is the perpendicular component of the force, effectively calculated as F × sin(θ), where θ is the angle between the force and radius direction.

Finding the perpendicular component allows