Wheels: why size matters
Children often wobble a lot when they ride bikes. Why is this?
- Is it just that they are not as good as adults at riding bikes?
- Why does their stability improve when they get a a bigger bike? Are they simply getting better at cycling?
- Why can I, when drunk, ride a bike better than a sober child?
The reason is, that every bicycle comes equipped with a pair of gyroscopes that stabilize the bicycle, and keep it going upright and in a straight line. The amount of angular momentum stored in a bicycle wheel depends on the size of the wheel, but how?
Angular momentum of wheels of different sizes
Let’s consider two bikes 1 and 2 being ridden at the same speed. Each bike has wheels of different radii, constructed of the same material. The important quantity we need to calculate is the angular momentum of the wheel since it is responsible for the stabilizing torques.
The angular momentum about the rotation axis is
L=Iω- The moment of inertia of a bicycle wheel is (see HRW pp 249)
I=Mr2
- The mass of the wheel scales as
M∝rso that I∝r3
- If the two cyclists move at the same speed, then we can use v=rω to relate their velocities
r1ω1=r2ω2;
- Cobmined all these results we have
- So doubling the radius of a bicycle wheel increases the angular momentum, and hence the restoring torques that provide stability, by a factor four. This is why it is easier to ride a bike with bigger wheels.