Summary Key Notes, Formulas, and Cheatsheet for As and A level Physics
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Course
Unit 2 - Newtonian mechanics (9702)
Institution
CIE
Book
Cambridge International AS and A Level Physics Revision Guide
This document aims to provide students with a quick and easy go-to guide when preparing for As and A level Physics exams. It highlights all the key points and important information in each module of the Physics course. This can save students time and they can read only whats important. It also cont...
Key Notes, Formulas, and more for AS and A Level
Physics
(9702)
Physics CheatSheet
, Data 3. Action = equal and opposite reaction Impulse Volume is DIRECTLY related to Intensity
Scientific Method Uncertainty -can’t have only one force A change in momentum (how you feel p change) Volume is DIRECTLY related to Frequency
F a, b = - F b, a f standard = 1,000 Hz.
1. Observation * units (metrics) Normal Force
Force : F = m a F = m Δ v
Δt Intensity Range
2. Define the Problem * measuring - able to change until breaking point of Time : * hidden variable* Threshold of hearing (Io) = 1 x 10 -12 w / m 2
3. Test/Experiment * sig. figs. whatever it’s holding FΔt = mΔυ = Δp Threshold of sound = 1 w / m 2
4. Hypothesis * Data - acts perpendicularly to “holding” object Conservation of Momentum β = 10 log ( I )
5. Collect Data/Manipulate Manipulation - comes from ground (except water) In the absence of an external force, the total 1 x 10 -12 w / m 2
6. Conclusion Newtons momentum of a system is constant ”How many powers of 10 are in that number?”
Accuracy vs. Precision 1 N = 0. 225 lbs. Mass is constant m1 υ 1 + m2 υ 2 = m1 υ 1 + m2 υ 2 Decibel = w / m 2 .
Accuracy – closeness of results to a standard F= ma ------ Fw = mg N kg (/ 9. 8) Work ( J ) w / m2
Precision – closeness of results to each other Kg N (x 9. 8) * Need to apply force W=Fd Pitch and Tone
*use same piece of equipment to collect data* Friction (Ff) * implies motion I volume f pitch
Qualitative vs. Quantitative 1. two or more things must be touching Power ( watt -- w ) Notes and tones : pitch with recognizable frequencies
Qualitative – more on precision than accuracy 2. energy is transferred (heat, sound, etc) P = W . = (F d) Laws of Pitch:
Quantitative – numbers count and are important
Sig. Figs.
3. texture matters… NOT SURFACE AREA
μ = coefficent of friction (Ratio of
t
J = 1 w = N m = 1 kg m2
t
1. f is INDIRECTLY related to length
2.
2
parallel force to perp. Force) s s s
Addition and Subtraction: f is DIRECTLY related to tension (Ft)
μ = Ff (3 decimal places) 1 horse power = 746 w
*least # places after decimal
Multiplication:
*places after decimal count as sig. figs.
FN
Ff = μ m g Ff = Fw (on flat surface)
Energy
Ability to do work 3. f is INDIRECTLY related to diameter (d)
2 . 5 cm = 1 in
μ = tan θ (when υ is constant)
Pressure: P = Force/area
Mechanical: energy of motion or position
Kinetic (K) : motion 4. f is INDIRECTLY related to density (D)
4. opposes motion which causes decelleration K = ½ m υ 2 (J) Beats : the resultant interference pattern of 2 notes
Vectors Potential (U) : position close in frequency but not exact
Vectors (velocity) – has BOTH magnitude and direction 5. static – “starting Ff” not moving (rolling) U = m g h (J) (W = F d) Creat nodes (sharps and flats)
Scalars (speed) – has magnitude ONLY greater force than kinetic When not given distance…(or force) Doppler Effect : the apparent change in frequency of
*time, mass, volume kinetic – moving (rolling, sliding, fluid) W = ½ m υ 2 - ½ m υ o2 (W = ΔK) a sound due to the relative motion of either the observer
Metric System Abbr. (K final) – (K initial) or the source of both
Mm - km - hm - dkm - m Conservation of Energy Resonate : when you cause something to vibrate at
Equilibrium
dm - cm - mm - Mm(E-6) - nm(E-9) Energy change from one to the other w/o any net loss its natural frequency
------------------------------------------------------------------------------------------------------- Translational: the sum of forces equal zero
Mult. Component Vecctors Rotational: the sum of torques equals zero UTOP = KBOT (mgh = 1/2mv2) Music repeating wave pattern
1. 18m due S Complete: must have BOTH Noise no repeating wave pattern
Center of Gravity : center of distribution of mass Wave Motion Consonance sounds GOOD
2. 22m, 47deg. S of W
Torque Simple Harmonic Motion Dissonance sounds BAD
3. 10 m, 78deg. N of W
Force with leverage causes rotation A repeating motion in which the acceleration is Decibel:
4. 30 m due E
Leverage: distance from fulcrum to force directly related to the displacement (distance away from I B .
*(W&E) Sum of the
*Directly related to torque the equilibrium) and always directed towards 1 x 10 –12 0 db
Vχ= (0)+ (-22 cos47)+(-10 cos78)+(30) =12. 9m
τ = F (perp.) l equilibrium. 1 x 10 –11
10 db
*(N&S) Sum of the
-------------------------------------------------------------------------------------------------------
Vχ= (-18)+ (-22 sin47)+(10 sin78)+(0) =-24. 3m -
1 x 10 –10 20 db
*Resultant υ = Circular Motion --- ---
–2
((12. 9)2 + (24. 3)2)1/2 =27. 5m Moving at a constant speed while accelerating f = 1/T 1 x 10 100 db
* θ = tan-1(24. 3) A = v speed: constant Cosine Curves 1 x 10 –1 110 db
(12.9) = 62.0deg dxn: constantly changing Y = A cosB (x – C) + D 1 120 db
R= 28m, 62deg S of E A = amplitude ( 0) : how much energy it has Natural Frequencies l = 170 / Hz
------------------------------------------------------------------------------------------------------- Centripetal Acceleration CosB = period ( 2 PIE / t) : time, 1 oscillation Brass/String n name synm wavl (λ) l f
Inward seeking Ac = υ 2 . C = horz. Shift : human error f fund. 1st har. 2l ½ λ v/2l
Kinematics r D = vert. Shift : distance, to x-axis f 2 1st ov. 2nd har. l λ v/l
Displacement Centripetal Force Waves f 3 2nd ov. 3rd har. 2/3l 3/2 λ 3v/2l
If + it’s AWAY Causes centripetal acceleration * Graphed SHM, transfer of energy f 4 3rd ov. 4th har. 1/2l 2 λ 2v/ l
If – it’s TOWARD Fc = m Ac (F = m a) Vibration : WORK to get energy fn= n υ hn = 2 l fn = Nf1
Fc = m υ 2 . (N) Propagates : what energy moves through 2l n
Velocity (m/s)
r Mechanical (light) Electromagnetic (sound) Woodwind n name synm wavl (λ) l f
Use ONLY when SPEED is CONSTANT
You MUST have cent. F to keep something Needs a medium does NOT need a medium f fund. 1st har. 4l 1/4 λ v/4l
1. does not include acceleration
moving in a circle More dense – better less dense – better f 2 ------ ------- ----- ----- ----
2. does not include starting and stopping
Centrifugal: body’s interpretation of cent. F Mechanical Waves f 3 1st ov. 2rd har. 4/3l 3/4 λ 3v/4l
in the same place
Transverse : medium vibrates perp. to energy f 4 ------ ------- ----- ----- ----
DOES NOT EXIST feels inertia
Most common ex. Guitar string, slinky f 5 2nd ov. 3rd har. 4/5l 5/4 λ 5v/4l
v= χ Rotation: spinning on axis within object
Longitudinal : medium vibrates para. to energy fn=nυ hn = 4 l
t Revolution: spinning on axis outside of object
Has compressions ex: sound 4l n
Acceleration (m/s/s) Linear / Angular
Surface : both para. and perp. to energy Instruments
*speeding up or slowing down Linear : speed = distance / time radius matters
“physics bob” ex: earthquakes, waves String
a= v 57. 3deg = 1 RADIAN
Principle of Superposition Produced by: plucking string, bowing
t 1 rotation = 2 π Radians = 360 degrees
Constructive Interference : added Change pitch : length, diameter, tension, density
Kinematic Formulas Angular: speed = # rotations or revolutions / time
Deconstructive : subtracting (adding negatives) Brass
X Direction Y Direction radius does NOT matter
V= λ_ V = λf Produce by : buzzing mouth piece
υ=υo+at -gt * by doubling the angular speed
2 T Change pitch : length of pipe (valves), buzzing
χ = χ o + Vo t + ½ a t -½gt2 you double the # of rotations
Standing Wave Woodwind
χ = χ o + ½ (υ + υ o) t ------ Linear Angular
A continuous wave train of equal amplitude (RAD), Produced by : reed vibrating
υ 2 = υ o 2 + 2 a ( χ - χ o) -2g( χ (m) χ=rθ θ (RAD)
wavelength (m), and frequ. (Hz) (/sec) in the same Change pitch : pads, holes
Change χ (o) to Y(o) υ (m/s) υ = r ω ω (RAD / s)
medium creating nodes and antinodes. Edge tones: narrow streams of air split by edge
Projectial Motion a (m/s/s) a = r α α (RAD / s / s)
Boundary : change in medium Helmholtz Resonance: edge tone with bottle (open
Half F (N) Ft = τ τ (Nm)
(part of energy gets reflected, part gets absorbed) hole)
* Y determines time in air Mass (m) I (mr)
rigidity : how much energy gets ABSORBED ---------------------------------------------------------------------
*compliment angles of 45deg have same range F=ma τ=Iα
close rigidity more absorbed Light
X . . Y . For linear ω=ωo+αt
different rigidity more reflected Particle Wave
χ=Vχt Y=½gt2 See other corner θ = θo + ω o t + ½ α t 2
Interference in Diffraction + Newton said so + Thomas Young – 2 slit ex
T= χ θ = θ o + ½ (ω + ω o) t
Crest + crest = antinode Crest + troph = node + Beams / Waves + reflection, refraction,
Vχ ω 2 = ω o 2 + 2 α (θ - θ o) ------------------------------------------------------------------------------------------------------- + travel in straight lines diffraction, interference
Full Rotational Inertia -
+Hertz – light is energy
* 45deg has max. range Resistance to begin or stop rotation Sound + Einstein – wave particle duality
Steps: A range of longitudinal wave frequ. to which the
1. υ o cos θ o / υ o sin θ o
• Depends on amount of mass AND where human ear is sensitive
Polarized Light: Light oriented to one plane (calc.)
Liquid Filter Display : lets only one degree of light in
it is placed Infra sonic sonic spectrum ultra sonic Visible Spectrum :
2. Find the TIME (check Y) (below 20 Hz. ) (20 Hz – 20,000 Hz) (20,000 Hz +)
Solid Sphere 2/5 mr2 Solid Disk ½ mr2 Radio * Micro * Infrared * Ultraviolet * Xrays* Gamma
3. Find the height / range
X . Y . Hollow Sphere 2/3 mr 2 Hollow Disk 1 mr2
• Velocity is indirectly related to Inertia
1. production : needs vibration Big wavelength Small wavelength
Red Orange Yellow Green Blue Indigo Violet
χ=Vχ t t= 2υo .
(Vx = υ o cos θ o) g • Shape of object spinning makes the 2. transition : needs a medium air Transparent: see through it and light passes
(Windows, glass)
(V o = υ o sin θ o) difference while spinning
y max = υ o 2 3 Forces acting upon an object in circular motion 3. reception : must be heard Translucent: can NOT see through it, light passes
(frosted glass)
2g
--------------------------------------------------------------------- 1. Centripetal Acceleration (Ac)
V sound = 340 m/s
V sound = 331 + . 6 (Temp.)
Opaque : can NOT see through it, NO light passes
Source: makes and emits light
Force (N) 2. Angular Acceleration (α)
Intensity : measurable
How loud a sound is * the time of flow of energy
Luminous: sun
- Causes a change in motion (causes acceleration) 3. Linear Acceleration ( a ) Luminate: moon
per unit area
- Is a VECTOR quantity ------------------------------------------------------------------------------------------------------- Light Year: takes 8. 3 min. to get light from sun
- I = Pow . ( P=W)
Equilibrium – no acceleration , forces cancel , “at rest” Dispersion: breaking up light into colors (prism)
Amp t
Newton’s Laws of Motion Colors
Conservation Laws Intensity is DIRECTLY related to amplitude
1. An object at rest will remain at rest until acted Cones in eye pick up 3 primary colors of light
Momentum ( N s ) Damping : further you get from the center quieter Additive
upon by an outside force Moving inertia (Newton’s 2nd law) it will be
INERTIA – directly related to mass Primary Secondary
Momentum IS inertia…Inertia is NOT momentum Inverse Square Law : I1 r12 = I2 r22 BLUE YELLOW
2. Acceleration is directly related to Force
Momentum is DIRECTLY related to mass and speed
p = m υ (N s)
RED
GREEN
CYAN
MAGENTA
indirectly related to mass • causes body to want to fly off tangent Volume (B): subjective (decibels)
F=ma (1 kg m / s2 = 1 Newton) * More than one light source
Relative Intensity Level loudness level
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