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Driving in Circles
Suppose you are driving slowly in a large empty parking lot. You hold the steering wheel at a fixed angle (so the front wheels are at a fixed angle to the car) and drive slowly forward, making a large circle. The rear wheels don't rotate, keeping zero angle with the car.
Getting Started
- Draw a careful picture of this situation. How can you locate
the center of the circular path on the picture just from the
direction of the wheels?
- How much diffence is there between the length of the path
of the inside and the outside wheels?
Going Deeper How much do the wheels "slip" (that is, what is
the difference between the direction the wheels are
pointed and the direction the car goes?) This is very
important to the handling of the car. How much does
this angle depend on the length and width of the car?
(Hint: You may want to start with a bicycle instead of
a car since a bike has zero width.)
Communicated by G. Hall.
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