Review of PHYS 150 Physics I
The world is 3-D. Some quantities can be expressed as a simple quantity, and these are
called scalars. Other quantities include not only a magnitude but also a direction, and
these are called vectors. We can add vectors nicely in rectangular form (x,y,z). We
can express vectors nicely in spherical form: (r, ) . If we only need 2 dimensions,
the spherical reduces to polar: (r,).
For motion we have two basic definitions: v = dx/dt; and a = dv/dt. (If we are working
in more than one dimension, then we must work in rectangular form: vx = dx/dt; vy = dy/
dt.) If the acceleration (in any rectangular component) is constant, then these
definitions lead directly by integration to: v = vo + at, and x = xo + vot + ½ at2 . For
uniform circular motion, these definitions lead directly by differentiation to: v = r
and a = 2r . We also add in = 2f and f = 1/T .
To relate force to motion, we have Newton’s Second Law: F = ma where this
equation is valid for each of the rectangular components. In Physics I we considered
several forces: Newton’s Law of Gravity: Fg = GMm/r2 acting towards the center of the
other mass. Contact force, Fc, which balances forces to keep them from breaking the
object, and this force always acts perpendicular to the surface. Sometimes this contact
force is called the Normal Force since it acts perpendicular (normal) to the surface.
Friction force, Ff, which balances up to a point and beyond that point is constant and
equal to Fc. The friction force acts parallel to the surface. Spring Force, Fs = -k(x-xo).
Newton's Third Law states that for every action there is an equal and opposite reaction. I
like to restate this law as "You can't push yourself. You can only push other objects and
hope that they push back." This is important in determining whether forces are ON
objects or are BY objects. Only forces ON objects are included in Newton's Second Law:
F = ma.
In principle, Newton’s Laws predict everything. In practice, it is often hard to actually
solve the equations because they are differential equations (that is, the F’s are functions
of x, v (which is dx/dt), and t and are related to mass times acceleration (which is d2x/dt2).
To solve some problems, we employ the concept of Work = ∫F•ds . By considering each
force, we can usually come up with a potential energy for that force, and by considering
the ma term in Newton’s Second Law, we can come up with the Kinetic Energy. The
Law of Conservation of Energy makes this useful: Ei = Ef . Kinetic Energy is KE =
½ mv2. Gravitational potential energy near the earth’s surface is PEg = mgh, and more
generally PEg = -GMm/r . Spring potential energy = ½ k(x-xo)2 .
Power is defined to be the rate at which we use energy: P = dE/dt = F•v .
Momentum is p = mv, and it is useful in considering collisions and explosions. By
working with Newton’s Second Law and Third Law, we get the Conservation of
Momentum: pi = pf .
