Torque Calculator

Trigonometry · Axiom Academy

REAL WORLD Torque Calculator: Rotational Forces Discover how angle affects rotational force through interactive wrench simulation Ever struggled to loosen a tight bolt? You instinctively know that pulling perpendicular to the wrench works best, but pulling at an angle makes it harder. This isn't just intuition—it's trigonometry in action ! Torque measures how effectively a force causes rotation. It depends on three factors: the force applied, the distance from the pivot point (lever arm), and crucially— the angle at which you apply the force. Adjust the force magnitude and the angle at which you apply it. Watch how the torque changes! The torque formula reveals why angle matters so much: r = Lever arm length (distance from pivot) θ = Angle between force and lever arm Key Insight: The Sine Function The sin(θ) term extracts the perpendicular component of the force. Only force perpendicular to the lever arm creates rotation. Force parallel to the lever arm has no rotational effect! Now that you've experimented with the simulation, answer this: At what angle does the force produce ZERO torque? Where You See This in Real Life Mechanics use longer wrenches (larger r ) and apply force perpendicular (θ = 90°) to maximize torque. This is why breaker bars are so effective! Pushing a door near the hinges (small r ) requires more force than pushing near the handle (large r ). Try it—the handle is positioned for maximum torque!

This is the written version of the interactive lesson above. See the full Trigonometry course.