for example it’s easier to use a long breaker bar than a shorter cresent wrench on lugnuts.
I don’t understand the torque and *why* it’s easier and why distance has to do with it.
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Think of a lever, like, a see-saw or something. If the ends are equal in length, you push down on one end and the other end goes up by the same amount. The amount of work you do pushing down your end is equal to the amount of work needed to lift the other end. Okay, now make one end super long, and the other super short. You push down on the long end, and the short end only rises a little, because it’s shorter; geometry prevents it from rising as much as your end went down. But the laws of physics say that the amount of work done still needs to be equal on both ends: momentum is conserved. So what gives? Well the short end rose with a lot more force. You applied some amount of force over a long distance, and that same momentum has to come back over the shorter distance of the other end, meaning more force per unit of distance needs to be applied. If you’ve played with a see-saw and people of different weight, you know this.
This is the basic principle of how levers work. You can multiply the amount of force applied by messing with the distances involved. A tool that rotates at one end like a wrench is essentially similar to a lever, except we’re talking angular momentum and torque: a longer wrench applies stronger torque. This makes intuitive sense if you think about it. The circumference of a bigger circle, is larger. So the path that you hand takes through space when you turn a longer wrench, is longer. And, assuming your arm applies the same force on a small or big wrench, there must be more work involved with the bigger wrench because your hand is moving further. But the other end of the wrench is moving the same amount, because of how angles work. So what happened to the extra work? It was exerted as increased torque, more twisting power.
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