Assignment 08.03 The Unit Circle Part I -Guided Notes

Around a Bike Wheel Let's consider the relationship between the angle of rotation for a point on a unit circle and the arc length made by a point rotating through the angle. A bicycle wheel has a 1-foot radius. The wheel rolls to the left (counterclockwise). l I I What is the circumference of this wheel? II P o C = m. C = 2(3.1z.)1foot. C is about 6.28 Now, let's add some points to the circle. Point Q is in the location where P will be after the wheel has rolled 1 foot to the left. The point, P, rotates through an angle of 1 radian to get to Q since 0 the radius of the wheel is 1 foot and it has rotated by 1 foot. g The point. R, is where point P will be after the wheel has rolled 3 feet to the left. The point R is in the second quadrant. The point, P, rotates through an angle of 3 radians to get to R because it has rotated a distance of 3 times die radius. In your guided notes questions 2 and 3 respond to the following: - Where will point P be after the wheel has traveled 7: feet to the left? What about 101: feet? 100:: feet? - After traveling some distance to the left, the point P is at the lowest location in its rotation. How far might the wheel have traveled?