Can you help a newster understand chainwheels and cassette numbers please?

[OakLeaf]

The chainrings are attached to your cranks, which are attached to your feet.

The cassette and its cogs are attached to the rear wheel.

However many links of the chain you pull with your cranks, the same number of links have to turn around the rear cog, since it's a loop. So for every rotation of your cranks (feet), the rear wheel turns the number of front teeth DIVIDED BY the number of rear teeth.

Let's say you have a single-speed bike with a 42 tooth chainring and a 21 tooth rear cog. For every rotation of your cranks (feet), you advance the chain 42 links. The chain must then also advance 42 links all the way around, which means it pulls the 21-tooth rear cog - and the attached rear wheel - TWO revolutions (42/21).

Derailleurs just let you change the number of teeth you're pulling front and rear. Obviously it's not always a nice round number, but it makes it easy to illustrate. Let's magically put a cassette and a rear derailleur on your imaginary bike now, but leave the same 42-tooth front. Shift into your 14-tooth rear cog. Now, for every revolution of your feet, your rear wheel travels THREE revolutions (42/14). This is a taller gear, because for every revolution of your legs, you're now pushing the bike half again as far as you were in the 21-tooth cog.

So when you shift to a taller gear, one of two things happens - either you keep the same cadence and start going faster (either with a greater effort over the same terrain, or with the same effort because you've started down a hill or gotten a tailwind); or you keep the same speed, but your cadence drops, because it takes fewer revolutions of your feet to go the same distance.

The reverse happens if you shift to a shorter (lower) gear.

That help?