Things You Should Know About Regents Physics
Measurement and Mathematics
Estimation: 1 kg = 2.2 lbs 1 apple = 1 N 1 quarter = 5 g = 0.005 kg
Order of magnitude: power of ten (thickness of paper = 10
-4
m)
Quantity Units Symbol
Length meter m
Mass kilogram kg
Time second s
Electric
current
ampere A
General Relationships:
Constant
y = c
Direct
y = mx
Slope = Δy/Δx
Linear
y = mx + b
Linear
(Indirect)
y = -mx + b
Inverse
y = c/x
Inverse-Square
(Quadratic)
y = c/x
2
Direct-Square
(Quadratic)
y = cx
2
Fundamental units
Scalars (magnitude only) Vectors (magnitude and direction) – only 9!
Distance
Speed
Anything else!
Velocity
Acceleration
Force (weight, normal force, etc.)
Momentum
Impulse
Fields (gravitational, electric, magnetic)
Graphs of Motion
d v
t t
Slope = velocity Slope = acceleration
Area = displacement
Two Types of Motion
Constant Velocity Constant Acceleration
Forces are balanced Forces are unbalanced
F
net
= 0, a = 0 F
net
≠ 0, a ≠ 0
In equilibrium not in equilibrium
Newton’s first law Newton’s second law
Distance v. Speed v. Acceleration v. Distance v. Speed v. Acceleration v.
time time time time time time
Projectiles
Horizontal Launch Angle Launch
x
Y
d
h
t
the same
a
0
9.81
v
i
v
i
0
v
f
v
i
v
avg
v
i
Horizontal – constant speed
Vertical – constant acceleration
x
Y
d
t
whole half
a
0
9.81
v
i
V
x
V
y
v
f
V
x
0 (top)
v
avg
V
x
sin
cos
tan
opp
hyp
adj
hyp
opp
adj
θ
θ
θ
=
=
=
Things You Should Know About Regents Physics
Mechanics
Equilibrium: no net force, no acceleration, constant velocity or at rest, forces
form a closed figure
Concurrent vectors: placed tail-to-tail
Component vectors: must be head-to-tail to find resultant
Resultant force = F
net
: head-to-head and tail-to-tail with components
Range of possible resultants:
Maximum = sum of vectors Minimum = difference of vectors
Equilibrant: equal and opposite to resultant
Box on a Hill in Equilibrium: mgsinθ = F
f
or F
A
or F
T
and mgcosθ = F
N
Mass (m): = inertia, amount of matter, constant from place to place, units: kg
Weight (F
g
): = force of gravity, changes from place to place, units: N
Formula:
F
g
= mg
Vectors
Resultant
Concurrent
Equilibrant
Maximum 2 5 7
Θ = 0
0
Minimum 2 5 3
Θ = 180
0
Triangle rule sum of any 2 sides ≥ third side
for forces to be in equilibrium
Inclined Plane
F
G
F
A
F
F
F
T
F
N
F
┴
= m g cosθ
F
║
= m g sinθ
Two names for little “g”:
1) acceleration due to gravity, units: m/s
2
, formula: g = GM/r
2
2) gravitational field strength, units: N/kg, formula: g = F
g
/m
Conservation Laws: electric charge, momentum, mass and energy
Circular Motion
v
F
c,
a
c
π
= = =
= = =
22
2
c cc
d circumferen ce r
v
t period T
v mv
a F ma
rr
Friction
Static friction (at rest) = applied force until motion starts
Kinetic friction (in motion) is constant
Maximum static friction is greater than kinetic friction
F
f
= μF
N
Newton’s Third Law:
Whenever A exerts force on B, B exerts equal/opposite
force on A. (Action/reaction pairs: bat and ball, Earth and Moon, hammer and nail)
Forces are the same but the effects of the forces are not:
ma = ma
Newton’s Law of
Universal Gravitation
12
2
g
Gm m
F
r
=
Things You Should Know About Regents Physics
Collisions
Conservation of Momentum: p
before
= p
after
Isolated System: no external forces
Elastic Collision: total KE is conserved
Sticky m
1
v
1
+ m
2
v
2
= (m
1
+ m
2
) v
f
(inelastic)
Bouncy m
1
v
1
+ m
2
v
2 =
m
1
v
1
+ m
2
v
2
(elastic)
Remember – Moving to the left gets a NEGATIVE sign!
Explosion
Equal and opposite forces, impulses,
changes in momentum, and contact times
Different speed based on mass
ma=Ma
m
v=Mv
Energy
Work: force and displacement must be parallel
W = Fd
Mechanical Energy: PE
g
+ PE
s
+ KE
Total Energy: PE
g
+ PE
s
+ KE + Q
Internal Energy = Q: thermal energy, heat due to
friction/air resistance
Power: rate of change of energy, rate of dong work
(units: Watts (W) = J/s)
PE
g
increases if height increases. KE increases if
speed increases.
PE
s
increases if spring is stretched
or compressed.
Formulas for springs: PE
s
= ½ kx
2
F
s
= kx
k = spring constant (units: N/m)
Conservation of Energy: E
T
= E
T
PE
g
+ PE
s
+ KE + Q = PE
g
+ PE
s
+ KE + Q
Work-Energy Theorem: W = ΔE
T
Electricity
Conductors (metals) have free electrons, insulators do not.
Objects become charged by losing or gaining electrons (not protons).
Elementary Charge: proton or electron
1 Coulomb of charge = 6.25 x 10
18
elementary charges
Charge of Electron: q = -1e OR q = -1.60 x 10
-19
C
Mass of Electron: m = 9.11 x 10
-31
kg
Charge of Proton: q = +1e OR q = +1.60 x 10
-19
C
Mass of Proton: m = 1.67 x 10
-27
kg
If two or more identical charged spheres touch, the final charge on each
is the average charge (total charge ∕ # of spheres). The total charge is
conserved.
A neutral object will be attracted (never repelled) by any charged object.
If two objects attract, they could have opposite charges or one could be
neutral. If two objects repel, they must have the same type of charge.
Charging by conduction: direct contact - electroscope gets same charge as rod
Charging by induction: no direct contact - electroscope gets charge opposite of rod
Coulomb’s Law
(electric force,
electrostatic force)
12
2
e
kq q
F
r
=
Electric Field
(units: N/C or V/m)
Lines go from + to -.
Lines never cross.
Lines show direction of force on small positive test
charge.
Field is most intense where field lines are most dense.
e
F
E
q
=
Things You Should Know About Regents Physics
Electric potential difference (voltage): work done per unit charge (V = W/q)
Resistance of a wire: R = ρL/A where A = πr
2
Least resistance (best conductor): short, fat, cold
Most resistance (worst conductor): long, skinny, hot
Potential difference
V
Volt
V = J/C
Current I Amps A = C/s
Resistance R Ohms Ω = V/A
Power P Watts W = J/s
Charge q Coulombs C
Energy W Joules J = N∙m
Voltmeter:
connect in parallel, infinite internal resistance
Ammeter: connect in series, zero internal resistance
Series Circuit
Parallel Circuit
Control: current stays the same
Resistance adds up (greater than greatest)
Adding extra resistor increases total
resistance and decreases total current.
Control: voltage stays the same
Resistance adds down (less than least)
Adding extra resistor decreases total
resistance and increases total current.
e 123
123
R
q
T
RRR
V VVV
=++
=++
123
e 123
1 111
R
T
q
I III
RRR
=++
=++
Resistance: R = V/I
Ohmic Device: follows
Ohm’s law (Vα I at constant T)
= constant resistance
Non-Ohmic Device: resistance
not constant (eg. filament lamp)
Slope = 1/R
Slope = R
Mechanical Power: P = W/t = Fd/t = Fv
Electrical Power: P = VI = I
2
R = V
2
/R
1 electronvolt (eV) = 1.60 x 10
-19
J
1 kilowatt hour = (1000 W)(1 hr) = 3.6 x 10
6
J
Three units of energy: joules, electronvolts, kilowatt hours
Magnetic Fields
From N to S, density = strength (intensity)
Direction of lines = direction of compass needle
Two Principles of Electromagnetism:
1) An electric current (or moving charged particle)
generates a magnetic field.
2) A changing/moving magnetic field induces an
electric current (electromagnetic induction).
Things You Should Know About Regents Physics
Order of Electromagnetic Spectrum
:
Source – accelerating charged particles
Radioactive Monkeys In Virginia Use X-ray Guns –
lowest to highest frequency and energy
Waves
Transverse:
perpendicular
Mechanical:
needs medium
Electromagnetic: no medium
Longitudinal:
parallel
Sound
Longitudinal, mechanical
Speed =
331 m/s (STP) 340 m/s (room temp)
Amplitude = loudness (volume)
Frequency = pitch
Energy α amplitude
Speeds up when going from air to water
Can’t be polarized
Light
Transverse, electromagnetic
Speed = c = 3.00 x 10
8
m/s (vacuum)
Amplitude α brightness (intensity)
Frequency α energy (E =hf)
Slows down when going from air to water
Can be polarized
Red: long wavelength, low frequency
Blue: short wavelength, high frequency
Radio Wave: electromagnetic
wave – speed = 3.00 x 10
8
m/s
Period (T):
seconds/cycle
Frequency (f): cycles/second
Wave equation: v = fλ
In Phase: A, E, I
Out of Phase by
180
0
or λ/2: A, C
Hard reflection: out of phase
Soft reflection: in phase
In one medium : f α 1/λ
Control: speed - you can only
change the speed of the wave by
changing the properties of the
medium)
Crossing a boundary: v α λ
Control: frequency stays the
same, so does period and phase
Constructive interference: in phase
Destructive interference: out of phase
θ
i
θ
r
Law of Reflection: θ
i
= θ
r
Diffraction:
bending around
obstacle or spreading through opening
Noticeable diffraction: when size
of opening approx. equal to size of
wavelength – as opening gets smaller,
more diffraction effects
Resonance:
energy is transferred to
a system by making it vibrate at its
natural frequency resulting in large
amplitude standing waves
Examples: guitar strings, bridges,
swings, wine glasses
Standing Wave:
Two identical waves traveling
in opposite directions in the same medium interfere
Fundamental Wave:
lowest frequency (f
1
),
λ
1
= 8.0 m
Constant
high
frequency,
Increasing
amplitude
Doppler Effect:
apparent change in frequency
due to relative motion
Constant
low
frequency,
Decreasing
amplitude
Doppler Shift for Light:
“blue shift” = object moving towards
“red shift” = object moving away
Refraction:
changing direction
when changing speed when
crossing a boundary
FAST:
into fast, bend away from normal
(high n to low n)
into slow, bend towards normal
(low n to high n)
Light slows down, bends towards
the normal, and has a shorter
wavelength when it enters a
medium with a higher index. The
frequency stays the same.
Visible Light:
400 nm (violet) – 700 nm (red)
Things You Should Know About Regents Physics
Double Slit Diffraction and
Interference: equally spaced
bright and dark bands
Red
Spread
Single Slit Diffraction: wide
and bright central maximum
Dispersion:
spreading out of
light into components due to
refraction – each color has slightly
different index and speed
Blue Bends Best - slowest
Red Resists Refraction - fastest
Total Internal Reflection
Critical Angle (θ
C
): incident angle for
which the refracted angle is 90
0
Formula: sin θ
C
= n
2
/n
1
Total Internal Reflection: all light is
reflected at surface, none is refracted – only
occurs when light travels from high to low
index and incident angle is greater than θ
C
Major use: fiber optic cables
Polarization
Only transverse waves can be polarized
– light = yes, sound = no.
Polarized Light: vibrates in only one direction
Natural Polarization: light is partially polarized
when it reflects off a surface
50% of unpolarized light transmits through a single
polarizer.
Parallel polarizers: 50% passes through both
Perpendicular polarizers: 0% passes through second
Modern Physics
Slope = Planck’s constant (h)
E = mc
2
(only use if E is in Joules and m is in kg)
1 u = 9.31 x 10
2
MeV
Hadrons made of quarks, leptons don’t break down further…
Antimatter = same mass, opposite charge
Alpha particle = helium nucleus (2 protons and 2 neutrons)
Positron = anti-electron = positive electron
Proton = uud
Neutron = udd
Fundamental forces:
EM and gravity – long-range; Strong and weak – short-range
(E
photon
= E
i
- E
f
)