Question

5. A return to the circular disc problem examined in class (Lecture 2): (Despite all of the text below you are required to do very little. Please read on.) A thin, circular plate assumed to lie on the ry-plane is rotating about its center O, located at (0, 0), with constant angular speed w. (w > 0 means that the plate is rotating in the counterclockwise direction.) Using the results obtained in class, show that the velocity field of of this plate is given by Here, (x, y) denotes the coordinates of a point with respect to a stationary Cartesian coordinate system in the room the so-called "lab frame" with origin at O. In class, the following analysis was employed: Consider an arbitrary point P on the rotating turntable. As the plate rotates, the point P traces out a circular trajectory in the lab frame which may be parametrized as x(t) = (r(t), y(t)), where z(t) r cos(wt + %) and y(t) r sin(wt +Bo) where r is the radius of the trajectory and 6o is suitably defined. Use the above information to show Eq. (1) by computing v(t)-x'(), etc.. (The derivation is actually quite short, i.e., one or two lines. You don't have to do anything else.

Answer 1

We can easily find the velocity of any point on disc by diffentiating the position of that point with respect to time as solved below