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

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

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.

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

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

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

The Fundamental Forces The fundamental forces: Gravity: large scale phenomena Electroweak force Electromagnetic force: everyday phenomena Weak (nuclear) force Strong (nuclear) force

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.