Physics 51
"Study Guide" for Final
("Laundry List" of important concepts)
Todd Sauke
Concept
(important
concepts
in
bold; vectors
also shown in
bold
)
Symbol or Equation
Prerequisites:
Physics quantities are typ. either scalars or
vectors
(magnitude & direction)
components
of vectors add
From
mechanics
, total external
force
on a body
= mass
x
acceleration
Σ
F
ext
=
m
a
(SI newton, "N")
Mass
(SI kilogram, "kg") resists change in motion (via "
momentum"
,
p
)
p
= m
v
,
F
ext
= d
p
/dt
A mass moving in a circle undergoes
centripetal acceleration
a
centr
= v
2
/ r
Conservation of linear momentum
: Isolated system (
Σ
F
ext
= 0)
Æ
Δ
p
=0 ;
p
f
=
p
i
m
1
v
f1
+ m
2
v
f2
= m
1
v
i1
+ m
2
v
i2
A moving mass has energy of motion, "
Kinetic Energy
" (SI joule, "J")
KE = ½ m v
2
(a scalar)
A spring being compressed pushes back proportional to compression
F
= - k
x
A compressed spring has energy of compression, elastic "
Potential Energy
" U = ½ k x
2
For conservative forces, mechanical energy is conserved
E
=
KE+PE
=
constant
(W
nc
=0)
Electromagnetics:
Electric Charge
is the fundamental quantity in Electrostatics
Q
(SI coulomb, "C")
Charge is conserved, quantized, and comes in "positive" and "negative"
e = 1.602 x 10
-19
C
Like charges repel (
radially
); opposite charges attract;
Coulomb's Law
F = (1/4
π
ε
0
) q
1
q
2
/ r
2
The constant
ε
0
is numerically related (by definition) to the speed of light, c
ε
0
=
10
7
/
(4
π
c
2
)
=
8.854
x
10
-12
All "normal" matter is made up of
protons, neutrons
and
electrons
m
p
= 1.67 x 10
-27
kg
Protons have +e charge; electrons have –e. Their mutual attraction holds
m
e
= 9.11 x 10
-31
kg
everything together.
In a conductor, electrons are free to move around.
Total force (
vector
) is the vector sum of individual forces (
superposition
)
F
=
Σ
F
i
The Electric field vector is the force per unit charge on a "test charge", q
0
E
=
F
0
/ q
0
F
= q
E
For distributions of charge (eg.
λ
,
σ
), vector integrate over the distribution
E
=
∫
d
E =
∫
dq
/
(4
π
ε
0
r
2
)
ř
Field lines
provide a graphical
representation
of
E
(and
B
) fields
E strong where lines are dense
An
Electric Dipole
is a separation of equal magnitude, opposite charges
p
= q
d
(
d
=separation -
Æ
+)
An Electric Dipole,
p
, in an Electric field,
E
, experiences a torque
τ
= p
x
E
τ
= p E sin(
φ
)
An Electric Dipole oriented in an Electric field has potential energy, U
U = -
p
•
E
= -p E cos(
φ
)
Electric Flux
; "flow" of
E
through a surface. (d
A
is a
vector
┴
to surface)
Φ
Ε
=
∫
E
• d
A
(through surface)
Gauss's Law
expresses the fact that the source of (static) flux is charge
Φ
Ε
=
∫
E
• d
A
= Q
encl
/
ε
0
Charge on a conductor at rest resides on its
surface
.
Also for conductor
Æ
E
inside
=
0
(for
static
case)
Use Gauss's Law to determine
E
field for
symmetric
charge distributions
eg.
E =
σ
/ 2
ε
0
(for sheet)
Gauss's Law easily shows E from a line of charge (instead of nasty integral)
E =
λ
/ (2
π
ε
0
r)
A symmetric distribution will be easier to solve for E using Gauss's Law