The Advent Calendar of Physics: Torque

Today’s advent calendar post was delayed by severe online retail issues last night and child care today, but I didn’t want to let the day pass completely without physics, so here’s the next equation in our countdown to Newton’s birthday:


This is the final piece of the story of angular momentum, the undefined symbol from the right-hand side of the angular momentum principle: torque is defined as the cross-product between the radius vector pointing out from the axis of rotation to the point where the force is applied, and the vector force that acts at that point. As with the definition of angular momentum, the simple, friendly-looking notation hides a lot of complexity: torque, like angular momentum, is a vector quantity, and points in a direction perpendicular to the force and the radius.

So, why is this important?

Torque is the rotational analogue of force: when you apply a force to an object, you cause its momentum to change in the direction of that force; when you apply a torque to an object, you cause its angular momentum to change in the direction of that torque. Torque is more complicated than force, though, as you can tell from the fact that it requires its own definition. Force is intuitive enough that you don’t need to say much more, but torque combines force and distance in a way that isn’t as obvious.

The effects of torque are all around us, though, from really obvious mechanical applications like the long handles on wrenches used to tighten big bolts– a moderate force applied at the end of the long handle produces a really big torque– to things that are so simple you would never think there was physics behind them, like the position of doorknobs. The knob on an ordinary door is always at the opposite side from the hinges, because a force applied there creates the biggest torque, and is thus the most effective for making the door swing open.

Torque is also the basis for one of the most critically important of simple machines: the lever. If you want to shift something really heavy, you do it by taking a long stick, wedging one end under the object to be moved, and prying it up, often using a small object as a fulcrum. This works because of torque: when you push down on one end of the stick, you’re trying to make it rotate, applying a torque about the fulcrum; the weight of the object you’re trying to move tries to prevent the rotation, producing a torque in the opposite direction. If the stick is long enough, though, and the fulcurm is close to the object to be moved, a relatively small force out at the end can produce a much bigger torque than a huge weight acting very close to the fulcrum. Thus, Archimedes’ immortal boast that given a place to stand, he could move the entire Earth with a lever.

The vector character or torque also has some cool consequences, such as the fun gyroscope tricks seen in this video:

(The narration is a little soporific, but can be ignored.) The trick where you suspend one end of a gyroscope, and it rotates about that point, rather than falling down, is a consequence of the vector nature of torque. The force of gravity acts downward, while the radius vector that goes into the torque points along the axis of the gyroscope. The cross product between these has to be perpendicular to both, so the direction of the torque produced by gravity is at right angles to gravity.

This doesn’t matter if the gyroscope isn’t spinning, but when it’s in motion, it has angular momentum that is directed along the axis of rotation. The torque cause by gravity causes the angular momentum to move not in the direction of the force of gravity, but in the direction of the torque. thus, the gyroscope axis moves horizontally, not vertically.

So, take a moment to appreciate the many cool properties and applications of torque, which is about so much more than just making things spin. And come back tomorrow for another equation of the season.

3 thoughts on “The Advent Calendar of Physics: Torque

  1. Cool video. Does anyone know of a video similar to this where the gyroscope is a bicycle wheel? We used it all the time, and it was big enough to use when we analyzed simple harmonic motion. Big arguments in class about who would get to take the spinning bicycle wheel “for a walk” down the hallway.

  2. the url is down for a third-phase construction. agree the second half of equation hides the complexity. in that a materials scientist via physics believes it only hides complex potential functions that could & should be applicable to many science and technology applications and functionality; more or less respectively, with many potential cross-transitional innovations. from quantum combos useful in QFT, Astrophysics, propulsion & imaging as well as directionally,and the more or less new exciting sub-discipline of Quantum Chemistry. in some considerations such properties are being utlized in both current faster computing via spintronics and just maybe in true pre-quantum technologies. off hand i am not sure if it would be useful in true quantum computing. however it could help in some way to prevent degradation and thus processing of “true” QIP methods. this will allow tuning to maintain apparent randomness and temporal isolation of QDs-subsystems to maintain the quantum-info until it is once again free to interact with other quantum-packets of info. in all of the previouly proposed ideas in using basics and evolutionary modified gyroscope-uses in this realm of the torque and force it will require the manufacture of gyroscopics based on advanced and adaptive materials able to interface with “tune materials” coupled to interact with external devices made of modified compound or natural constituents. one very promising innovative contraption is the ‘quantum motor’ under patent by researchers in Europe working on the project for a major automobile producer. whether or not the device is truely of a quantum nature, it does use quantum and quantum-like methods. interaction with proper attuned gyroscopic torque materials could possibly enhance functionality and alleviate the degradation-local of the quantum motor’s quantum nature. finally with proper adjustments from tunable gyroscope it would be possible to eliminate periodic global-degradation for very extended periods of real-time in real-world uses.

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