Suppose a reflector is attached to a 26 inch diameter bike wheel, 8 inches from the center. If...

Question:

Suppose a reflector is attached to a 26 inch diameter bike wheel, 8 inches from the center.

If the bike wheel rolls without slipping, find parametric equations for the position of the reflector.

Parametric Equation

This problem is based on the concept of parametric equations. The familiarity with the concept of parametric equations of the conic sections can be a big help. Also, while solving these types of problems it is preferable to draw picture so that we have a clearer understanding of the problem.

Answer and Explanation:


The picture below shows the reflector:

From the figure, it is quite easy to understand that the reflector is connected 8 inches away from the center and when the wheel rotates it is quite obvious that the reflector will rotate as well in a circular motion with a radius of 8 inches.

  • Therefore, it is a circle with a radius of 8 inches.

The required parametric equation can be given as,

{eq}\displaystyle \boxed{\displaystyle x=8\cos t} {/eq}

{eq}\displaystyle \boxed{\displaystyle y=8\sin t} {/eq}

Where {eq}\displaystyle t \in [0,2\pi] {/eq}.


Learn more about this topic:

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Evaluating Parametric Equations: Process & Examples

from Precalculus: High School

Chapter 24 / Lesson 3
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