When an object is in equilibrium, we know that the sum of all external forces acting on it is zero. An unbalanced force causes an object to accelerate in the direction of this force. However, forces can result in more than acceleration in a given direction. Forces can cause rigid objects to rotate. This is where the concept of a torque comes from.
A torque, simply put is a force applied to a rigid body at a certain distance from a piviot point. We know from grade nine science that with levers, the longer the arm, the less force it takes to move it a certain distance. This is the principle of torques. A longer lever or other rigid body yields a greater torque. A larger force also yields a greater torque. To better understand this principle, see the first examply below. The symbol for torque is the Greek letter the lower case Tau, which looks much like Pi, with one of the strokes that extends from the tail missing. To calculate a torque, one multiplies the force applied to the rigid body by the perpendicular distance between the applied force and the pivot point which is also called the lever arm. This yields the extremely important torque formula:
Since torque is equal to Force which is expressed in Newtons times the perpendicular distance expressed in meters, the SI unit for torque is a Newton meter or N*m. It is also important to note that when an object rotates in a counter-clockwise direction due to a torque, the torque is expressed positively, while an object rotating in a clockwise direction has a negative torque. Remembering this will be important later on.
Now, let's look at a diagram to better understand what I just explained, some definitions of important terms used in describing torques and look at some examples. After that, you'll be able to try some practice problems for this section.
Let's look at a door handle now to help better understand the concept of a torque. We have all opened doors in our lives, but usually from the handle. Have you ever tried opening a door from the middle or close to the hinges? Seems silly, but if you try it, you'll know that it is harder. No just because there is no handle, but because you are closer to the hinges, or piviot point. If you are closer to the handle, you need a greater force to generate the necessary torque to open the door. Below are some diagrams of this concept.
A. 
B. 
C. 
D. 
In examing these pictures, we need to use some termanolgy that goes with the concepts of torques.
Line of Action: This is the imaginary line on which the force acts.
Axis of Rotation: This is the fixed point about which the system rotates. In the above case, it would be the hinges.
Lever Arm: This is the perpindular distance from the line of action. It is the distance you use in the formula Torque = F * l
First lets have a look at picture A.
In this example, we see that the line of action on which the force is applied directly perpendicular to door and thus the length of the door would be the lever arm. Thus to calculate the torque here, you would multiple the force by the length of the door as in this case it is the lever arm.
Next let's examine picture B.
Now this case is slightly different from that of A. While the door is still perpendicular to the applied force, the force is being applied is closer to the axis of rotation. This means the the lever arm is shorter than the door and would be the distance marked in the above picture. Since in this case, the distance from the piviot point is less, the torque will be less, explaining why it is much harder to open a door closer to the hinges.
Now, examine case C.
In this case we have a force for which the line of action is directly along the door pointing towards the axis of rotation. Looking at this there is no perpendicular distance between line of action and the axis of rotation, since the line of action is directly in line with the axis of rotation. This means the value of the lever arm is 0, which translates to no torque. When you think about it though, this makes sense. If you apply a force to a door in a straight line with the hinges, the door is not going to rotate. No rotation means no torque.
Finally, we'll look at example D.
In this final example, the force on the door is being applied on an angle with the door instead of straight from it. This means that the door is no longer the lever arm as the line of action is not perpendicular to it. Now we have a new value for the perpendicular distance between the axis of rotation and the line of action. The lever arm in this case isn't something concrete like a door. The lever arm is an imaginary line drawn into the diagram in this case. You can find this new value using simple trig, since the line of action forms a right triangle with the rest of the system. Then simply use that value in the torque formula to calculate the torque.
Problems For You To Try
