POSITION AND COORDINATES l to specify a position, need: reference point (“origin”) O, distance from origin direction from origin (to define direction, need reference direction(s) l position along a line: position specified by one (signed) number l position in a plane: position of point P specified by length of “vector” OP (distance)and angle of OP with respect to reference direction, or by two numbers x,y l position in 3-dimensional space: need a third number (e.g. height above the x-y plane) l coordinates: = set of numbers to describe position of a point

VECTORS AND SCALARS l physical quantities can be “scalars”, “vectors”, l “tensors”, l s calar : quantity for whose specification one number is sufficient; examples: mass, charge, energy, temperature, volume, density l vector : quantity for whose specification one needs:  magnitude (one number)  direction (number of numbers depends on dimension) numbers specifying vector: “components of the vector” in suitably chosen coordinate system; e.g. components of the position vector: numbers specifying the position; examples: position vector, velocity, acceleration, momentum, force, electric field,.. magnitude = “length of vector” e.g.  distance from reference point” = magnitude of position vector,  “speed” = magnitude of velocity.

velocity l velocity: = (change in position)/(time interval) average velocity = velocity evaluated over finite (possibly long) time interval v av =  x/  t,  x = total distance travelled during time interval  t (including speeding up, slowing down, stops,...); instantaneous velocity = velocity measured over very short time interval ;  ideally,  t = 0, i.e. time interval of zero length: v = limit of (  x/  t) for  t  0;  t  0 is limit of  t becoming “infinitesimally small”, “  t approaches zero”, “  t goes to zero”; note that velocity is really a vector quantity (have considered motion in only one dimension) difference quotient:  x/  t = “difference quotient” of position with respect to time difference quotient = ratio of two differences; limit for  t  0: [limit of (  x/  t) for  t  0] = dt/dx = “differential quotient”, also called “derivative of x with respect to t” “differential calculus” = branch of mathematics, about how to calculate differential quotients. l angular velocity  : (change in angle)/(time interval)  = 2  f (f = frequency of rotation)

ACCELERATION l acceleration = rate of change of velocity a = (change in velocity)/time interval average acceleration a av =  v/  t,  v = change in velocity  t = duration of time interval for this change instantaneous acceleration = limit of average acceleration for infinitesimally short time interval, a = dv/dt acceleration, like velocity, is really a vector quantity change of velocity without change of speed:  if only direction changes, with speed staying the same;  e.g. circular motion if a = 0: no acceleration,  velocity constant  “uniform motion” motion in straight line with constant speed l angular acceleration = rate of change of angular velocity