Do gyroscopic forces from the wheels make any significant contribution to the rideability of a bicycle?

Asked by: Steve Collier

Answer

Yes, the gyroscopic forces, better known as the angular momentum, of the wheels on a bike
allow us to ride a bike.
Any object which is spinning about an axis such as wheels, tops, gyroscopes, fans, etc.show
the property of angular momentum.

To understand angular momentum, you must understand torque. Torque is what you do to a door
when you push it open, or turn the knob. Anytime there is something that swings or spins
about a fixed point, a torque must be applied to change the motion of that object. Torques
are applied to a lever arm which is the perpendicular distance from the axis of rotation to
the line that the force is acting on, therefore the lever arm is a vector like the force.
Torque is then defined as the cross product of the lever arm and the force. An alternate
definition of torque is the rate of change of angular momentum. Because torque is a cross
product of vectors, the direction of the torque is perpendicular to the directions of the
force and lever arm. The direction for torque and therefore angular momentum is given by
the right-hand-rule.

The reason that you stay up on a bike is that angular momentum, like regular momentum, must
be conserved if no external torques act on the object. Because angular momentum is a
vector, not only must its magnitude be conserved, but also its direction. This implies that
any change in the orientation of the object will change the vector for angular momentum.
Therefore, tops stay up because the angular momentum wants to stay conserved in the same
direction.

When you are riding a bike forward, the right hand rule gives the direction of angular
momentum to be to the left, perpendicular to the wheel. This direction does not want to
change, therefore the wheel wants to stay upright and it makes the bike very ridable. Have
you noticed it is harder to ride a slow bike? Because the wheels are moving slow, the
angular momentum is less and the direction of rotation is easily changed. I have seen a
bicycle built with an extra wheel that did not touch the ground so that it could be spun
forwards or backwards so that it either added to or subtracted from the total angular
momentum of the bike. When the extra wheel was spun in the same direction as the other
wheels, the bike was extremely easy to ride even at low speeds. However, when the extra
wheel was spun backwards, the bike became almost impossible to ride because the vectors for
angular momentum cancelled each other out. It was like trying to balance a bike that was
not moving.

I hope this answers the question about riding a bike. Could we possibly make intermediate
training wheels that do not touch the ground, but add to the ridability of a bike?
Answered by: Matthew Allen, B.S., Physics/Calculus Teacher St. Scholastica Academy

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