I had a random Archimedes quote come to me randomly today, and conveniently, it ties to some physics concepts which I will be covering in this post.
This image is horribly disproportionate but it gets the point across.
Using these principles, Archimedes brought up this interesting proposal where he famously quoted “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” Though this proposition may sound insane, once you look at the equation that represents torque, τ=rFsinθ (Theta in this case is 90º), with r representing the distance from axis of rotation you can see that no matter how big the force is on one end, if the proportion of the distances(d¡/d¡¡)are equal to the proportion of forces(F¡¡/F¡) then the lever will balance out: assuming that it is massless (doesn’t have to be but then we have to factor in center of mass).
This is probably the most primitive application of torque there is but I believe it is a great introduction to it. Torque is probably one of the more interesting aspects of physics (at least to me) and there is a lot more difficult applications of it. Take this question for example: the ball has an weight of G (G=m*g), R represents the radius of the ball, l is the length of a massless board, and you have to find the magnitude of F (everything is frictionless).
Although this example looks rather difficult (which it is), it uses the same concepts as the Archimedes torque lever and the application of some trigonometry. This question is just an example, but if you happen to want to torture yourself with this question, however, always remember the quote that the greatest physics teacher spams all the time: “Break it down, Break it down”- Mr. Glenn.
