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:
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.
- What are the parametric equations describing the location of the rider?
- Where is the rider after 18 seconds have elapsed?
- 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.
- As the point A makes one complete revolution, indicate in the picture the direction and range of motion of the point B.
- Find the coordinates of the point A as a function of time t.
- Find the coordinates of the point B as a function of time t.
- 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?).
- Find the first two times when the x-coordinate of the point B is 5.
- Write and solve one question about this situation.
As a side note, I have our tech trainer setting up a PD on Geogebra because lots of my mathies in my building are interested because of what we’ve done with our kids so far. I am SO thrilled!