Two of the most fundamental ideas in Physics are conservation of energy and conservation of momentum. However, energy and momentum are not quantities directly observable with our senses, not like time and space. Rather energy and momentum are inferred from measurements of directly observable quantities. For instance, by measuring the position as a function of time, we can determine velocity, and then, having previously measured the mass, we can infer the momentum of an object from the relation p=mv, or the kinetic energy from K.E. = ½ mv2. Thus, in order to achieve a better understanding of energy and momentum, we begin with the directly observable quantities of time, space, and mass, and interesting combinations of these quantities.
(Note: Our concept of time, space, and mass is greatly colored by the environment in which we live, and in more advanced Physics courses, will be subject to some modification. But, we must have someplace to begin, and our everyday feeling for these quantities is accurate for situations not so different from our environment, with similar velocities and masses.)
In this course you will be learning mechanics at a more sophisticated level than in introductory Physics. Although this is not a mathematics course, mathematics will be used, and reviewed as necessary. Calculus and vector algebra will be commonly used, and techniques for solving basic differential equations will be introduced.
length | meters (m) |
time | seconds (sec, s) |
mass | grams (g) |
other units for force, energy, torque, etc. are formed from combinations of the above.
x(t) = some function of time for instance x(t) = Asin(t) or x(t) = a+bt+ct2
The velocity is given by the derivative of x with respect to t.
v(t) = dx/dt = [xdot]
For the two relations for position as a function of time given above, the velocity as a function of time is:
v(t) = -Acos(t)
v(t) = b+2ct
Lastly, differentiating once more yields the acceleration.
a(t) = dv/dt = [vdot] = d2x/dt2 = [xdoubledot]
The two position functions give an acceleration of:
a(t) = -Asin(t)
a(t) = 2c