1 Honors Physics 1 Class 04 Fall 2013 Vectors Non-Cartesian coordinate systems Motion in multiple dimensions Uniform circular motion Applications

2 Activity – Motion with constraints Frictionless pulley and table. Only net external force=gravity on mass 2. Rope massless and fixed length. Find acceleration of mass 1.

3 Vectors Examples: Projectile motion; Uniform circular motion.

4 Cartesian coordinates

5 Cylindrical coordinates 5

6 Spherical coordinates 6

7 Exponentials and complex numbers Discuss powers, square roots, derivatives.

8 Newton’s Laws in 3d form

9 Motion Example: Projectile trajectory

10 Motion Example: Choosing coordinates well is important

11 Activity: Uniform circular motion Which way does a point? Which way does v point?

12 Activity: Application The Spinning Terror ride The spinning terror is a large vertical drum which spins so fast that everyone stays pinned to the wall when the floor drops out. For a typical ride the radius of the drum is 2 m. What is the minimum angular velocity if the coefficient of friction between the patron and the wall is 0.3?

13 Application example: Falling through a viscous fluid Assume that the density of the fluid is very small compared to the density of the falling object. (e.g – a human body in air) Assume that the body falls under the action of constant gravity and drag force only. Assume that the drag force is linear in speed: Is there a terminal velocity? If there is, find the terminal velocity.

14 Application example: Mass on a spring