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, q, f) .  If we only need 2 dimensions, the spherical reduces to polar: (r,q).

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 integration to:  v = wr  and  a = w2r .  We also add in w = 2pf  and  f = 1/T .

To relate force to motion, we have Newton’s Second Law:  SF = 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 mFc.  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: SF = 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:  SEi = SEf .  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:  Spi = Spf  as long as we can ignore outside forces, or the time interval between the initial and final momenta is very small.

We also considered rotations and found that there are analogous laws and equations for rotations as there are for regular motion.

w = dq/dt  (just like v = dx/dt)  KErot = ½ Iw2  (just like KE = ½ mv2)

a = dw/dt  (just like a = dv/dt)  L = Iw  (just like p = mv)

St = Ia  (just like SF = ma)

Homework Problems:

Problem #1: Do the computer homework program: Motion Graphs on Vol. 1 (Your best score counts. In this case you do not have to worry about limiting cases or approximate numerical solutions.)

Problem #2: Do the computer homework program: Gravitational Deflection (Trajectories) on Vol. 1. (Your best score counts. In this case you do not have to worry about limiting cases or approximate numerical solutions.)

Problem #3: Do the computer homework program: Newton's 2nd Law on Vol 1. (Your best score counts. In this case you do not have to worry about limiting cases or approximate numerical solutions.)