A Staff Report from the Straight Dope Science Advisory Board

Why is it easier to balance on a moving bike than a non-moving one?

January 29, 2002

Please see the update to this Staff Report: http://www.straightdope.com/mailbag/mbicycle.html

Dear Straight Dope:

Why is balancing on an unmoving bicycle so much harder than balancing on a moving bicycle?

Because modern bicycles are equipped with a pair of  gyroscopic stabilization devices that require the motion of the bike in order to operate. These devices are known as "wheels."

What is a gyroscope and how does its stabilizing power work? A gyroscope is just something spinning. A spinning object has angular momentum, whose magnitude is dependent on the speed of rotation, the mass of the object, and the distribution of that mass with respect to the axis of rotation. Angular momentum, like its homely cousin linear momentum, is conserved. For our purposes this means that once a gyroscope gets lined up in a certain way, it wants to stay lined up. That, in short, is how gyroscopic stabilization works.

Angular momentum is a vector quantity--it points in a definite direction. For example, a rolling coin has a different direction of angular momentum than a coin spinning like a top. The trouble with angular momentum is that, since it involves something that's turning, often it's not obvious what that direction is.

Fortunately, physicists have come up with a convention for the direction of angular momentum that makes angular momentum physics easy. This convention is known as the Right Hand Rule. Using your right hand, curl your fingers in the direction an object is spinning. Your thumb points in the direction of the angular momentum vector. (There are cross products and moments of inertia and other fancy physics stuff involved--if you're sufficiently fascinated, get a book or take a physics course.)

So let's look at that bike. Using your right hand, curl your fingers in the direction the bike wheels are spinning--forward and around. You should find your thumb pointing to the left. OK, now extend your left arm straight out to the left and point your left index finger. This represents the angular momentum vector of your bike wheels. Unfortunately, sticking your arm out like that also throws off your balance. Oh no, you start to tip over to the left! (Go ahead, tilt to the left--you didn't think you could do physics without waving your arms around, did you?) Notice that your wheels' angular momentum vector (i.e., your left arm) is no longer pointing directly left, but rather at some angle towards the ground. The angular momentum vector of your wheels has changed, but that's a problem because angular momentum is conserved. You need to acquire some other component of angular momentum to ensure conservation. To restore the original angular momentum of your untilted bike, you need to add a vector quantity in the "up" direction to your tilted left arm. What does that mean in terms of motion? The Right Hand Rule tells us. Using your right hand, stick your thumb in the upward direction to represent the additional angular momentum you need. Your fingers are curling around to the left. Thus, your bike will turn to the left to conserve angular momentum.

That was a whole lot of physics and gymnastics to conclude what every 7-year-old knows: when you lean your bike left left, you turn left. The magic of physics. The gyroscopic effect tends to convert a tipping-over motion into a left- or right-turning motion. You can see why gyroscopes are handy as stabilization devices in boats, where turning is preferable to tipping over.

On a moving bike, it's fairly easy to recover from a left- or right-turning motion: you can steer the bike or lean the other way. On a non-moving bike, a tipping motion is converted, thanks to gravity, into an even faster tipping motion. Your only recourse is to quickly throw your center-of-mass around to try to keep it over the bicycle's base, and since the base of a bike is very narrow, this is hard to do, especially since tipping over tends to move your center of mass rapidly off your base.

OK, you may lower your arms and sit down now. Some people think it's funny to see a physics teacher flapping around illustrating angular momentum. (I had one student ask me if I used to be a cheerleader.)  You know what's funnier? Seeing an entire auditorium full of freshman physics students applying the Right Hand Rule during a physics exam. Even funnier? One student in the second row using his left hand.

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