Rotational Motion

Example on the Right Hand Rule

Question
Which direction is the torque in this diagram, with respect to the pivot point labelled O?

Figure 1 Diagram of the problem

Figure 2 Diagram of the problem, force has been translated in order to simplify the use of the right hand rule

Solution
Here we are assuming that the force, F, and moment arm, r vectors were originally placed 'head-to-head' (that is, F was pointing to the arrowhead of r, not at its pivot point). This is shown in Figure 1. However, by translating the force vector to its position in Figure 2, the use of the Right Hand Rule becomes more obvious.

Without this clarification, it is possible to interpret Figure 2 as having the force vector going through the pivot point, in which case there would be no torque (see What is Torque?). This is due to the definition of the moment arm, which is the distance between the pivot point and the point where the force acts. If the force acts right on the pivot point, then r = 0, so there would be no torque. (Having a moment arm of zero would be like trying to open a door by pushing on its hinges; nothing happens because no torque has resulted from the applied force.)
Recall the use of the Right Hand Rule in torque calculations. Fingers are to point in the direction of the first vector, and are curled towards the second vector. In this case, torque is the cross product of the moment arm and torque. So the fingers would point to in the same direction as the moment arm, and are curled to the direction of the force (clockwise). The direction of your thumb is the direction of torque; in this case, torque is into the screen.

We can represent "into" and "out of" using symbols when drawing three-dimensional diagrams. The symbol for "into" is  (it's supposed to be the tail of an arrow), and for "out of" is  (this is the tip of the arrowhead).

Figure 3 indicates the direction of torque using the "into" symbol (shown in blue).


Figure 3 Diagram of the solved problem (resulting torque is into the screen)


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