1. Summary for Chapters 2  4 Kinematics: Average velocity (Instantaneous) velocity  Average acceleration = (Instantaneous) acceleration = Constant acceleration:

2. See Appendix A (page A-5) for a list of common derivatives.

3. Vectors Vector = Quantity with magnitude & direction. Free vectors: All vectors with the same magnitude & direction are equivalent. Linear combination of vectors A & B : ,  numbers Linear independence : A & B are linearly independent if     0 Vector space : Set of vectors that include every possible linear combinations among themselves. Basis : Set of maximum number of independent vectors in the vector space. Dimension : Number of vectors in the basis. Every vector in the vector space can be represented as a linear combination of the basis vectors.

4. Vector Arithmetic with Unit Vectors Cartesian coordinate system: basis = rectilinear orthogonal unit vectors

5. 2-D constant acceleration : ( centripetal )  Uniform circular motion : Projectile

6. Newton’s 1 st law of motion (definition of inertia frame) : Newton’s 2 nd law of motion: Newton’s 3 rd law: Normal force n : contact force acting normal to contact surface. m in f = m a is the inertia mass (same everywhere). Weight = force of gravity on mass: m is gravitational mass in inertial frame

7. The Fundamental Forces The fundamental forces: Gravity: large scale phenomena Electroweak force Electromagnetic force: everyday phenomena Weak (nuclear) force Strong (nuclear) force 1 10 25 10 36 10 38

8. Free Body Force Diagram Keep only features relevant to the dynamics. Replace all objects by points upon which forces act. Represent all forces by vectors.