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I realize this seems like a pretty simple issue of drawing a free body diagram, but I just can't seem to figure it out.

If a bike leans, then it must have had a torque that made it lean. I considered the centripetal force, in this case friction, as a possible source for this torque, but that would create torque in the opposite direction. The only remaining torque causing force in my FBD is weight. But weight was there before the leaning, and would only cause a torque after leaning.

If anything, because of centripetal acceleration, observing from an inertial frame of reference, the bike should lean in the opposite direction because of the introduction of the centripetal force. So the question is, what force causes the bike to start leaning?

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  • $\begingroup$ Related: physics.stackexchange.com/q/24/2451 and links therein. $\endgroup$
    – Qmechanic
    Nov 18, 2017 at 12:23
  • $\begingroup$ Do you ever ride hands off? You lean to make the bike turn, not the other way around. $\endgroup$
    – The Photon
    Nov 18, 2017 at 15:12
  • $\begingroup$ @ThePhoton It actually can affect the other in both ways. You use the handlebars to create the lean. If you ride no hands, you actually give a little "jiggle", which because of the angle of the handle-bar stem, causes counter steering to occur by virtue of moving the bike. $\endgroup$
    – AER
    Nov 18, 2017 at 15:27

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Two things that need to be considered. Often it is not the cyclists weight that causes the lean in. Subconsciously, as people learn to ride a bike, they do something called counter-steering.

So for example coming in to turn right, a cyclist will quickly turn the handlebars left to lean the bike to the right due to centripetal acceleration. Once the lean has been achieved, the handlebars are then turned to the right to turn and balance the bike in a turn. Then to upright the bike, the handlebars are turned slightly harder in until it levels (due to increasing the centripetal force outwards relative to the lean), then the bike is straightened, and the handlebars follow.

People don't believe that they do this, it's quite funny.

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  • $\begingroup$ I see, but how would this account for the case of a speeding car? If a car turns a bend too quickly, I imagine it will also lean, and in fact often it will over turn. Does the driver unconsciously veer to the opposite side before making a turn? $\endgroup$
    – Clovis Nyu
    Nov 18, 2017 at 12:39
  • $\begingroup$ @ClovisNyu do a web search on counter steering. Cars don't need to lean, because of their side by side wheel base, to counteract torque from centripetal acceleration around a corner. $\endgroup$
    – AER
    Nov 18, 2017 at 12:43
  • $\begingroup$ Yea, did a search, drew out a FBD, I'm pretty sure they lean given that the turn is fast enough. There's something called the "Moose Crash Test" where the driver makes a suddenly turn to test whether the car will overturn. Maybe I'm confusing something here... $\endgroup$
    – Clovis Nyu
    Nov 18, 2017 at 12:54
  • $\begingroup$ @ClovisNyu Do you understand countersteering? That is what causes the lean largely. $\endgroup$
    – AER
    Nov 18, 2017 at 13:26
  • $\begingroup$ Hmm, so the car won't lean if there is no counter-steering? I think I'm starting to see it. If the driver doesn't counter-steer and just makes a sudden turn, he will just skid. But this raises more questions as I'm currently working on a problem that claims that past a certain angular velocity, the outer wheels will lift off the ground and the car will roll. $\endgroup$
    – Clovis Nyu
    Nov 18, 2017 at 14:10
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The bike would lean in the other direction, due to centripetal force, without a cyclist. A cyclist leans the bike on purpose into the turn, to counteract said centripetal force.

The torque involved is the cyclist's weight as they lean into the turn.

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