Advanced Math/Cycloid

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Expert: - 10/12/2010


Question
How can the path of the mark on the wheel of a bicycle that has a radius of 2 units traveling at a speed of 1 unit per second over a period of t seconds be found using trigonometry?

Answer

Cycloid
Questioner:   Megan
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Trig. Functions
Question:  How can the path of the mark on the wheel of a bicycle that has a radius of 2 units traveling at a speed of 1 unit per second over a period of t seconds be found using trigonometry?
 
See attached picture.  
x1 = r cos(90 - theta) = - r sin t

y1 = r sin(90 - theta) = - r cos t

x = s + x1 = s + r sin t

y = r + y1 = r - r cos t


What you get is a cycloid, see:

http://en.wikipedia.org/wiki/Cycloid

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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