Chapter 4.1, Problem 1fT

In the space at right sketch the position vectors for point C at the beginning and at the end of a small time interval t.

1. Label the change in angle $\left(\Delta \theta \right)$ and the distance between the center of the wheel and point $C\left(r_c\right)$ . Sketch the path taken by point C during this time interval.

What is the distance that point C travels during $\Delta t$ ?Express your answer in terms of $r_c$ and $\Delta \theta$ .

2. Use our answer above and the definition of linear speed u., derive an algebraic expression for the linear speed of point C in terms of the angular speed $\omega$ of the wheel.

What does your equation imply about the relative linear speeds for points farther and farther out on the wheel? Is this consistent with your answer to part A?