Force is casually defined in physics as a push or a pull. The effects of an applied force are obvious: to cause motion, to stop motion, and to deform an object. Torque is a special name given to a force that causes things to turn, twist, or bend. Such as when you are turning the steering wheel of your car. It would be weird – wouldn’t it, to say that you are pulling the steering wheel of your car to the right instead of turning the steering wheel. It gives an impression of someone trying to rip off the steering wheel, and nobody wants that! “Turn” is the word, and “Torque” is the technical word for it. In fact, the word “Torque” has its origins in the Latin language where it means to “twist” or “turn”.
What is the difference between torque and force?
Of course, the difference between torque and force (or as you might prefer: a push or a pull) goes beyond the choice of words. The difference can be summed up in one statement, “all torque is a result of a push or a pull, but not all push or pull results in torque (turn)”. For example, you can push into the steering wheel as long you like, but it won’t budge – might piss off the neighbors with the honking though! For the steering wheel to turn, you have to know how (and where) to apply that push.
Torque in physics depends on the following:
Location: the turning effect of an object depends on where the force is applied. There’s a good reason the handle of a hinged door is placed far from the hinge line. Also, someone who is serious about kicking open a closed door will be sure to kick it as far from the hinge line as possible, preferably at the handle – go figure!
Magnitude: You don’t usually kick the door open when sneaking out at night do you? The door may fly open so violently slamming onto the adjacent wall and give you away or piss off the neighbours – again. Common sense dictates that you push the door very gently with a force just necessary to open it. The turning effect of a rotating body depends on the magnitude of force impressed upon it.
On this note, you are also advised to keep both hands on the steering while driving as it gives you more control of the torque you impress on the wheel; a sharp turn is easily achieved with both hands turning the wheel than a single one.
Direction: One man arrived home so drunk that instead of pushing the door open, he tried to lift it from the bottom up – like a rollup door of a garage. Legend says the man slept on porch that day. Moral of the story: the magnitude of force and location do not matter as much if not properly directed. For best results in turning a hinged door, push at right angles to the hinge line.
Formula for Torque
These three important conditions: Force, direction, and position are summarized in the following mathematical relation used to define torque:
In the above equation,
- The Greek letter tau, 𝜏 represents the torque
- r is the position vector (accounts for the location, measured in units of distance from the axis of rotation)
- F is the force
- And the little arrows on top of them accounts for the direction.
Torque as a physical quantity is a vector. Meaning, it has both magnitude and direction and abides by the established laws of vector operations. (As I say, not all quantities with magnitude and direction are vectors – just as not all that glitters is gold). The equation above is what is known as the cross product of two vectors.
Magnitude of Torque
Someone I used to know was always holding a cup of coffee one hand and a stack of papers on the other. Of course, this guy hardly ever opened the office door with his hands – he’d elbow it open, or give it a soft kick at the bottom, or (my favourite) you push it open with his butt. In any case, he didn’t seem to give much thought as to how he got the door open, he just wanted to swing it open whichever way works. Usually, the door would open but with some extra difficulty. Because of his awkward demeanour, he would end up using more force than otherwise necessary to swing the door open.
In other words, not all the force exerted goes into turning the door open; some force is “lost” into a meaningless direction and does not play part in turning the door.
Consider the diagram below,
We have an arbitrary rigid body looking like a rod that is free to rotate about the z-axis. A force F is applied at a point P, located a distance r from the axis of rotation. As you might appreciate from the sense of rotation of the object, the force, F, isn’t in-line with the rotation of the body and therefore, only a part of it actually goes into turning the body. Much like someone elbowing a closed door.
To further this point, consider a cross-section slice on the x-y plane of the body. The initial force F is now resolved into its perpendicular components, represented here as the radial (FR) and tangential components (FT). In this arrangement, the vector r locates the force F relative to the (now) x-y plane.
Only one component here (FT) plays a role in turning the object, the other component (FR) being directed radially away from the axis of rotation, has no effect on the rotation of the body about the z-axis. The magnitude for “Torque” is then defined as the product of force and the perpendicular distance from the axis of rotation.
𝜏 = Force x Perpendicular distance
In this case, 𝜏 = rFsinθ
