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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You have more torque when you apply the force because it lets you apply the force over a larger distance. [Here’s a crude pic](https://i.imgur.com/SxoTa2i.png), but the point is: the longer the wrench, the bigger the difference between how far the wrench moves and how far the bolt moves. By compressing a long inch wrench turn into a short bolt turn, it multiplies the force.
(Less ELI5: work = force x distance. The work is constant and cannot disappear, so the bolt moving a shorter distance than the wrench handle where you’re pushing *must* experience a higher force)
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.
When you use a longer tool, you’re effectively increasing the distance from the pivot point where you’re applying your force. Even if you apply the same amount of force, the longer distance multiplies that force, making it much easier to turn the bolt.
You can think of using a tool like a wrench or a breaker bar as similar to using a see-saw. When you sit on a see-saw, if you’re sitting closer to the middle, you need to push harder with your legs to lift yourself up. But if you sit further away from the middle, it becomes easier to lift yourself up. This is due to leverage.
I’m not sure how else to put it but I hope it helps in some way.
Any type of leverage works as follows: imagine you have to put a bucket of water with 5kgs on a tablet but you can only lift 1kg with your muscles, so what you do is, lift 1kg 5 times and you have 5kg on the tablet. That’s how any leverage works, you trade, repetition, rotation, distance, and so on for work. At the end you will have the same amount of work done, or bit more due to inefficiencies. So when you are pedalling with a easy gear you are trading doing more work with more rotation to keep going. If you have strong muscles you can rotate less but put more effort in each stroke. At the end the sum will be the same. With a lever is the same. You will put less work by doing a wider movement on the handle for the lesser movement near the working point, so force is being added along the movement.
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