Expert: Sherry Wallin - 10/10/2010

Question
QUESTION: How do I find the function that describes the path of a mark on a bicycle wheel that has a radius of 2 units and is traveling at a speed of 1 unit per second over a period of t seconds?

ANSWER: Megan~

Think of the mark on the bicycle wheel as being on the circumference of a circle. This circle has a circumference of 2*pi*r or 2(2)pi = 4pi
The speed of this mark is: [distance traveled]/[time traveled] = f(t)
where f(t) = 4pi units/t sec

Math Prof

---------- FOLLOW-UP ----------

QUESTION: I'm sorry, I should have been more specific. I need to know how to find the TRIG function. Would it be y=2sin(t)?

Answer
On a circle with a radius of 2 you have x^2 + y^2 = 2^2 => that means that with x = cos t and y = sin t we have cos^2t + sin^2t = 4 => sqrt(cos^2t + sin^2t) = 2 and then with C = 2*pi*r then we have
2*pi*sqrt(cos^2t + sin^2t) is the distance traveled in one revolution and so f(t) = 2*pi*sqrt(cos^2t + sin^2t)/t

Math Prof