# PHY5210 W08

## Midterm Review

The exam will cover chapters 9 and 6.

### Mathematical Techniques

- Note that it is expected that you can handle vector algebra (addition, scalar multiplication, dot and cross products, componenets, unit vectors, and cartesian, cylindirical and spherical coordinates) and differentiation and integration involving vectors.
- angular velocity vector
- addition of angular velocities
- Rotating Coordinate Frames
- derivative of a vector: (d
**u**/dt)_{non-rotating} = (d**u**/dt)_{rotating} + **Ω** × **u**

- Calculus of variations: the Euler-Lagrange equation.
- square of path length, ds², in cartesian, cylindrical, and spherical coordinates.
- Constraints and the method of Lagrange multipliers.

### Physics Topics

- Linearly accelerating reference frame, fictitous force -m
**A**_{0}
- Rotating reference frame, fictitous forces
- Centrifugal force m
**Ω** × (**r** × **Ω**)
- Coriolis force 2m
**v** × **Ω**
- Transverse force m
**r** × d_{t}**Ω**

- Relation between ω and v for pure rolling
- Solving minimization / maximization problems with the Euler-Lagrange equation.

### Problem Sets 1 to 4

Review any questions on these problems.

© 2008 Robert Harr