PHY5210 W15

Exam 1 Review

The exam will cover chapters 9 and 6.

Mathematical Techniques

  1. 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.
  2. angular velocity vector
  3. addition of angular velocities
  4. Rotating Coordinate Frames
    1. derivative of a vector: (du/dt)non-rotating = (du/dt)rotating + Ω × u
  5. Calculus of variations: the Euler-Lagrange equation.
  6. square of path length, ds², in cartesian, cylindrical, and spherical coordinates.
  7. shortcut relation: v² = ds²/dt²

Physics Topics

  1. Linearly accelerating reference frame, fictitous force -mA0
  2. Rotating reference frame, fictitous forces
    1. Centrifugal force mΩ × (r × Ω)
    2. Coriolis force 2mv × Ω
    3. Transverse force m r × dtΩ
  3. Relation between ω and v for pure rolling
  4. Solving minimization / maximization problems with the Euler-Lagrange equation.
  5. Lagrangian Mechanics
    1. Determining the number of generalized coordinates
    2. Determining the Lagrangian, L = T - U, for those generalized coordinates
    3. Finding the motion with Lagrange's equation ∂L/∂qi - (d/dt)(∂L/∂qidot) = 0

Homeworks 1 to 3

Review all questions on these homeworks.

© 2015 Robert Harr