I was trying to explain to someone how the gears in a transmission work, specifically, how a gear with a greater circumference requires more power to start moving the car because you’re essentially asking one rotation of the engine to move the car a greater distance with a given inertia and that will require more force. As you can imagine, I wasn’t too happy with that explanation. Can anyone give me a simple analogy for this? I understand it, but not well enough to explain it clearly. It also got me wondering: Would a pully with a greater circumference “feel” harder to pull a given weight? If so, why?
I’m not a gearhead but you might consider the long pole extending from the old millstones that they used to turn it with. If you get way out near the end of the pole and push, it’ll turn pretty easily, but as you work your way in and eventually stand next to the stone and push, it takes progressively more effort.
Conversely, one you get it moving and inertia is with you, you can spin it relatively faster standing near the millstone while the speed that can be reached from out near the end reaches a finite practicality much sooner.
Gotta a ten speed bike handy?
Have the person start off in the lowest gear (smallest front, largest rear) ask them to note how easy it is to pedal, and how limited the top speed is. Bring the bike back and shift it into the higest gear (largest front, smallest rear) ask them to again pedal off from a stop. Be ready to catch them when they fall.
Same bike same weight, same road, the only difference is the gears.
Low gear = lots of revolutions for a given speed (pedals, or the engines), low top speed, easy to climb hills
High gear = few revolutions for a given speed, high top speed, hard to climb hills.
I’m looking for an analogy to explain the physics, not the phenomenom.
lieu - that’s kind of counterintuitive given that larger gears (farther out on the pole) are harder to start, not easier.
Gears are just a series of superimposed levers; concentrate on the interaction of one tooth on one gear and the interlocking tooth on the other - reduce this to a pair of levers, the pivot points of which are equivalent to the centre of the axle - do a few experiments with pivots and balances to demonstrate the concept of moments.
I’m not sure what you’re looking for as gears are often the analogy to explain other things because they are so simple to understand.
Without going into physics 101 let’s look at a lever and examine force vs displacement. If I have a lever with a fulcrum in the middle, a see-saw for example, I can press down on one end to lift a weight on the other end. Each end moves an equal distance with equal force in opposite directions. That is the equivalent of two gears with the same diameter and number of teeth.
If I place the fulcrom 1/3 of the total distance from the weight I want to lift I now have twice as much lever on my side as the opposite side. I can lift the weight by pressing down with half as much force but I have to move my side twice as far downward as the weight on the opposite end moves upward. This is equivalent to a small gear driving a bigger one with twice as many teeth. I have to rotate the small gear twice to make the big gear go around once but the torque on the output will be twice the force I place on the input.
I think I got stuck trying to put that concept and the changing inertia of the car in one analogy.
That is why I suggested the bicycle. After explaining the concept of a lever, demostrate a real world example on the bike.
A good demostration is worth many thousand words.
I didn’t really include inertia in the analogy as the seesaw is probably a poor example. I think I see what you’re getting at and we haven’t provided enough information.
There are some more factors involved if you have an internal combustion engine and that may be giving you trouble. Because of the nature of the engine it doesn’t produce an even power curve over RPM range. You need to keep the engine in a specifc RPM band to get best acceleration. Too slow and the engine may start “lugging” and running erratically, too fast and the power band may fall off or in some cases the engine may damage itself.
Starting out in first gear the engine’s RPM band is matched to a corresponding low speed range. The lowest gear (highest numerically) takes the input from the engine and gives output that favors torque for acceleration from a dead stop over speed.
When RPM gets too high we shift into second gear and RPM reduces to match road speed. The gear ratio is balanced slightly more in favor of speed but with less torque at the output. This continues with ever higher gears (lower numerically) until we get to an economical cruising speed that may have the engine turning at relatively low RPM.
This is all moot with an electric as they can produce full torque at any RPM.
You might do some searches on the physics definitions of force, energy, power and work which may help fit it all together for you.
I realize this isn’t what you’re looking for, but it could help you.