# Day 130: Going In Circles

Short post today as I hope to join the #Statschat on twitter…every Thursday night at 9pm EST hosted by Bob Lochel.

Today in Precalculus, we ventured into parametizing circular motion.  Good ol’ Geogebra to the rescue again!  I just have to send out a big THANKS to all of you who create and post such fabulous documents!  With little (to no) intervention from their teacher (why was I even there?!), my precalc scholars developed the parametric equations almost seamlessly based on their “playing” with the figures and sliders.  They were so quick that I had to ask them “what would happen if we wanted to go around the circle three times as fast?”  And they jumped on it like a bunch of math-jackals!  You can see in the fourth photo their almost immediate result.

Once they had the conceptual understanding, we moved into the practice/application phase of the lesson.  They worked on the following problems:

Merry-Go-Round Application

A rider jumps on a merry-go-round of radius 20 feet at the pictured location. The ride rotates at the constant angular speed of ω = -p/7 radians/second. The center of the platform is located 50 feet East and 50 feet North of the ticket booth for the ride.

1. What are the parametric equations describing the location of the rider?
2. Where is the rider after 18 seconds have elapsed?
3. How far from the ticket booth is the rider after 18 seconds have elapsed?

Applying Circular and Linear Motion

A six foot long rod is attached at one end A to a point on a wheel of radius 2 feet, centered at the origin. The other end B is free to move back and forth along the x-axis.  The point A is at (2, 0) at time t = 0, and the wheel rotates counterclockwise at 3 rev/sec.

1. As the point A makes one complete revolution, indicate in the picture the direction and range of motion of the point B.
2. Find the coordinates of the point A as a function of time t.
3. Find the coordinates of the point B as a function of time t.
4. What is the x-coordinate of the point B when t = 1? You should be able to find this two ways: with your function from part (c), and using some common sense (where is point A after one second?).
5. Find the first two times when the x-coordinate of the point B is 5.