[Physics] Why is it easier to go uphill on a lower gear

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In cars as well as bicycles, when we are on a lower gear, the driving wheel (the one on the wheels) has a bigger radius compared to when on a higher gear.

So on a lower gear the bike/car would move lesser compared to the higher gear for the same no. of revolutions of the engine.

Now my question is, why does that fact make it easier to go on a uphill on a smaller gear? Does that prevent slipping? Beacuse torque applied is more? Or what?

Can someone explain with a free body diagram?

Best Answer

The power input is roughly constant (that of a car is dictated by the total engine power while for a bicycle it depends on the user). The gear or similar tools adjusts the mechanical advantage so that a low gear will express the engine power in force rather than speed (recall that power is force times speed). On higher gears the force is traded in for speed.