Name: Richard A.
The physics of balancing a bicycle moving at speed would
seem to involve the effect of spin angular momentum but counter steering
at speed seems to involve effect of centripetal acceleration.
Can you clarify relative contributions of these effects?
I need to answer a student in non mathematical terms who asked me "how do
bicycles work?", meaning balance and steering. HELP!!! - He's brainier
Yes -- I went through the same thing and managed (finally) to figure it
Angular momentum is negligible. I convinced myself by mounting a weighted
bicycle wheel from our lecture hall on my bike. Whether on the front
(steerable) part or on the back part, it made no noticeable difference
even when spinning rapidly with at least 10 times the angular momentum
possible with the real wheels. Incidentally, if it had an effect, it
would be in the wrong direction! Turning the wheel to the left when
moving forward would cause the bike to lean to the right, as the right
hand rule will tell you. (Angular momentum of the wheel is to the left
and the torque is up.)
What then? Countersteering, as you mentioned. If you rotate the front
wheel to the RIGHT while moving forward, the ground exerts a force to the
RIGHT on the front wheel. This causes the bike to lean to the LEFT. If
you continue like that, you will fall to the left. To avoid that turn
the front wheel to the LEFT just enough so the torque due to the ground
now pushing to the LEFT keeps the bike at the proper angle. To stop the
turn, turn the front wheel more to the LEFT and the bike will straighten
If people do not believe you (as I find is usually the case) and they can
ride no-hands, tell them to push the right handlebar forward with the heel
of their right hand to turn the front wheel to the left. If they do not
cheat terribly, they will find that they have initiated a RIGHT turn!
They should be careful, as it is easily possible to oversteer in a way
most no-handers don't expect
Incidentally, no-handed turning is similar but more complicated and
depends on the fact that on a normal bike leaning the bike to the right
causes the front wheel to turn to the right. So to initiate a left turn,
lean your upper body to the LEFT. This make your lower body (and the bike
body) lean to the RIGHT, causing the front wheel to turn to the RIGHT.
This then makes the bike body lean left and see above.
I tested this by moving the front wheel forward so it turned left when the
bike was leaned to the right. I can guarantee you that that bike is NOT
What spin angular momentum does is make the bicycle easier to balance. A
large part of balancing a bike is remaining in an appropriate position.
All objects "prefer" to keep moving as they are. The wheels are spinning in
a vertical orientation, alligned with the path of the bicycle. The faster
they spin, the more difficult it is to change them. The bicycle is moving
forward. The faster it moves, the harder it is to make the body of the
bicycle change direction. A fast-moving bicycle with fast-spinning wheels
takes time to cause to change. While riding such a bicycle, as compared to
a slow bike, the rider has much more time to make slight adjustments in body
position to prevent the bike from falling over.
To turn the bicycle, you turn the handle bars: more difficult when the
wheels are spinning faster. Once turned, the front wheel moves to the side.
The body of the bike, however, tries to keep going forward. The "natural"
thing for the bike to do is fall down as the front wheel pulls out from
under it. The rider has to lean toward the inside of the turn to prevent
this from happening. If the bike "tries" to flip to the right, The rider
leans to the left to counter the effect.
This is how a bicycle works.
Dr. Ken Mellendorf
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Update: June 2012