Archive for March 26th, 2014

Vectors, Sin(ϴ), and the Torque Formula

Wednesday, March 26th, 2014

      Last time we introduced a physics concept known as torque and how it, together with modified gear ratios, can produce a mechanical advantage in devices whose motors utilize gear trains.   Now we’ll familiarize ourselves with torque’s mathematical formula, which involves some terminology, symbols, and concepts which you may not be familiar with, among them, vectors, and sin(ϴ).

Torque = Distance × Force × sin(ϴ)

      In this formula, Distance and Force are both vectors.   Generally speaking, a vector is a quantity that has both a magnitude — that is, any measured quantity associated with a vector, whether that be measured in pounds or inches or any other unit of measurement — and a direction.  Vectors are typically represented graphically in engineering and physics illustrations by pointing arrows.   The arrows are indicative of the directionality of the magnitudes involved.

      Sin(ϴ), pronounced sine thay-tah, is a function found within a field of mathematics known as trigonometry , which concerns itself with the lengths and angles of triangles.   ϴ, or thay-tah, is a Greek symbol used to represent the angle present between the Force and Distance vectors as they interact to create torque.   The value of sin(ϴ) depends upon the number of degrees in the angle ϴ. Sin(ϴ) can be found by measuring the angle ϴ, entering its value into a scientific calculator, and pressing the Sin button.

      We’ll dive into the math behind the vectors next time, when we return to our wrench and nut example and apply vector force quantities.