Physics Notes

1. Dot points out of the page.
2. Cross points into the page.

3. Angular Momentum of particles relative to a point (origin), angular momentum of rigid body
about fixed axis. (remember this thing)
4. Like the other two conservation laws that we have discussed, conservation of angular
momentum holds beyond the limitations of Newtonian mechanics. They hold for particles
whose speeds approach that of light (where the theory of special relativity reigns), and they
remain true in the world of subatomic particles (where quantum physics reigns). No
exceptions to the law of conservation of angular momentum have ever been found.
5. G is the gravitational constant: G = 6.67 * 10-11 N-m2/kg2
6. Since Module 5-1, we have assumed that Earth is an inertial frame by neglecting its rotation.
This simplification has allowed us to assume that the free-fall acceleration g of a particle is
the same as the particle’s gravitational acceleration (which we now call a g). Furthermore, we
assumed that g has the constant value 9.8 m/s 2 any place on Earth’s surface. However, any g
value measured at a given location will differ from the a g value calculated with Eq. 13-11 for
that location for three reasons: (1) Earth’s mass is not distributed uniformly, (2) Earth is not
a perfect sphere, and (3) Earth rotates. Moreover, because g differs from a g, the same three
reasons mean that the measured weight mg of a particle differs from the magnitude of the
gravitational force on the particle.
7. Coulomb’s law works for only charged particles (and a few other things that can be treated
as particles). For extended objects, with charge located in many different places, we need
more powerful techniques. So, here we consider just charged particles and not, say, two
charged cats.
8. Density of air decreases as we move up from ground.
9. You have seen that the excess charge on an isolated conductor moves entirely to the
conductor’s surface. However, unless the conductor is spherical, the charge does not
distribute itself uniformly.
10. The capacitance is a measure of how much charge must be put on the plates to produce a
certain potential difference between them: The greater the capacitance, the more charge is
required.
11. It is often contended that V=iR is a statement of Ohm’s law. That is not true! This equation is
the defining equation for resistance, and it applies to all conducting devices, whether they
obey Ohm’s law or not. If we measure the potential difference V across, and the current i
through, any device, even a pn junction diode, we can find its resistance at that value of V as
R=V/i. The essence of Ohm’s law, however, is that a plot of i versus V is linear; that is, R is
independent of V. We can generalize this for conducting materials by using (E=pJ)
12. The charging times for RC circuits are often stated in terms of t (time constant). For example,
a circuit with t=1us charges quickly while one with t=100 s charges much more slowly.
13. Note that a greater t means a greater discharge time for RC circuit.
14. Electric potential has meaning only for electric fields that are produced by static charges; it
has no meaning for electric fields that are produced by induction.
15. In the RLC, the source of energy is the alternating-current generator. Some of the energy
that it provides is stored in the electric field in the capacitor, some is stored in the magnetic
field in the inductor, and some is dissipated as thermal energy in the resistor. In steady-state
operation, the average stored energy remains constant. The net transfer of energy is thus
from the generator to the resistor, where energy is dissipated.
16. The process of finding the components of a vector is called resolving the vector.
17. Classification and comparison of motion is called kinematics.
18. Vector addition has two important properties. First, the order of addition does not matter.
Second, when there are more than two vectors, we can group them in any order as we add
them.
Above equations hold when angle measured counterclockwise from the positive x axis. If the
reference axis for the polar angle is chosen to be one other than the positive x axis or if the sense of
increasing is chosen differently, then the expressions relating the two sets of coordinates will change.
19. A unit vector is a vector that has a magnitude of exactly 1 and points in a particular direction.
It lacks both dimension and unit. Its sole purpose is to point—that is, to specify a direction.
20. The point is we have great freedom in choosing a coordinate system, because the relations
among vectors do not depend on the location of the origin or on the orientation of the axes
21. cos(a) = cos (360 – a) (so in scalar product either angle (smaller or larger can be used)
22. A dot product can be regarded as the product of two quantities: (1) the magnitude of one of
the vectors and (2) the scalar component of the second vector along the direction of the first
vector.
23. sin(a) = -sin (360 – a) (so in vector product only smaller angle can be used)
24. To check whether any xyz coordinate system is a right-handed coordinate system, use the
right-hand rule for the cross product I cross j=k with that system. If your fingers sweeping
(positive direction of x) into j (positive direction of y) with the outstretched thumb pointing in
the positive direction of z (not the negative direction), then the system is right-handed.
25. In general: A cross product gives a perpendicular vector, two perpendicular vectors have a
zero-dot product, and two vectors along the same axis have a zero-cross product.
26. Caution: When a position vector is drawn, as in Figs. 4-1 through 4-3, it is an arrow that
extends from one point (a “here”) to another point (a “there”). However, when a velocity
vector is drawn, as in Fig. 4-4, it does not extend from one point to another. Rather, it shows
the instantaneous direction of travel of a particle at the tail, and its length (representing the
velocity magnitude) can be drawn to any scale. Caution: When an acceleration vector is
drawn, as in Fig. 4-6, it does not extend from one position to another. Rather, it shows the
direction of acceleration for a particle located at its tail, and its length (representing the
acceleration magnitude) can be drawn to any scale.
27. If the velocity changes in either magnitude or direction (or both), the particle must have an
acceleration.
28. During its two-dimensional motion, the projectile’s position vector and velocity vector
change continuously, but its acceleration vector is constant and always directed vertically
downward. The projectile has no horizontal acceleration.
29. In projectile motion, the horizontal motion and the vertical motion are independent of each
other; that is, neither motion affects the other. This feature allows us to break up a problem
involving two-dimensional motion into two separate and easier one-dimensional problems,
one for the horizontal motion (with zero acceleration) and one for the vertical motion (with
constant downward acceleration).
30. Angle measured counterclockwise from positive x-axis is positive. Angle measured clockwise
from positive x axis is negative.
31. 1u (atomic mass unit) = 1.66 e-27 kg
32. The length (magnitude) of A×B is equal to the area of the parallelogram spanned by the
vectors A and B.
33. The volume V of the parallelepiped is given by
The product A⋅(B×C) is often referred to as a triple scalar product. It is a pseudo scalar. The term scalar
refers to the fact that the triple product is invariant under the same simultaneous rotation of A, B, and C.
The term pseudo refers to the fact that simultaneous inversion
A → −A, B → −B, and C → −C
converts the triple product into minus itself, while a proper scalar is invariant under inversion.
http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Vector_product.html#:~:text=A
%20proper%20vector%20changes%20sign,product%20is%20a%20pseudo%20vector.
34. A proper vector changes sign under inversion, while a cross product is invariant under inversion
[both factors of the cross product change sign and (−1)×(−1) = 1]. A vector that does not change
sign under inversion is called an axial vector or pseudo vector. Hence a cross product is a pseudo
vector. A vector that does change sign is often referred to as a polar vector in this context.
(answer to why cross product is called a pseudo vector)
35. Solution of past paper question using the law of cosines
https://www.slader.com/discussion/question/vectors-and-have-equal-magnitudes-of-500-the-sum-
of-and-is-the-vector-600-determine-the-angle-between-and-veca-vecb-hatj-3ffcf25f/
36. Although an ideal gas does not exist, any real gas approaches ideal behaviour if its density is
low enough.

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1. Dot points out of the page.

2. Cross points into the page.

A → −A, B → −B, and C → −C

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