Physics : Ultimate Review Guide

Unit 1 : 1-D Kinematics & Graphing

directly & inversely proportional

• directly proportional: when 2 quantities increase/decrease together

• inversely proportional: when 1 quantity increases & the other one decreases (and vice versa)

equations

• ∆x = v_it + 1/2at²

• v_f = v_i + at

• v_f² = v_i² + 2a∆x

• ∆x = 1/2(v_f + v_i)t

  • ∆x = displacement

  • v_i = initial velocity

  • v_f = final velocity

  • a = acceleration

  • t = time

position vs time graphs

• a line graph showing an object’s position at a given time

  • x-axis: time

  • y-axis: position

• slope gives object velocity

velocity vs time graphs

• a line graph showing an object’s velocity at any given time

  • x-axis: time

  • y-axis: velocity

• slope gives object acceleration

• area under the curve gives displacement

general rules

• for an object with a constant position, the velocity is 0

  • the velocity vs time graph is a horizontal line on the x-axis

• for an object with a constant velocity, the velocity vs time graph is a horizontal line at the value of the velocity

• for an object with a constant acceleration, the velocity vs time graph is a straight slanted line

Unit 2 : Forces & Newton’s Laws

force: any push/pull on an object

1st law of motion (law of inertia)

• an object at rest remains at rest & and an object in motion remains in motion unless acted upon by an unbalanced force

  • inertia: an object’s resistance to change

  • mass: amount of inertia an object has

    • weight ≠ mass

  • equilibrium: an object not acceleration (balanced forces)

    • static: an object at rest

    • dynamic: an object moving at a constantly velocity

2nd law of motion

• acceleration of an object is directly proportional to force & inversely proportional to mass

3rd law of motion

• whenever one object exerts a force on a second object, the second object exerts an equal but opposite force on the first object

4 fundamental forces _{(strongest → weakest)}

• nuclear force → electromagnetic force → weak nuclear force → gravity

2 types of forces

• contact & field (action at a distance)

  • contact: touching

  • field: not touching

    • weight: force of gravity pulling an object on a planet

    • normal: contact force that surfaces exert to not pass through each other

    • tension: pulling force on an object exerted by a rope

    • friction: opposes motion between two surfaces in contact

law of universal gravitation

• F_g = Gm₁m₂/r²

  • G = 6.67 × 10^-11

  • r = distance

hookes law

• spring force: force exerted by a compressed or stretched spring on any object it’s attached to

  • variable: F_s

  • unit: new tons

  • known as a restorative force

    • always wants to return to it’s equilibrium position

      • direction = whether spring is compressed/stretched

      • equilibrium length: length of a spring when not compressed/stretched

• hooke’s law: extension of a spring is directly proportional to the amount of force applied to it

  • F_s = k∆x

  • spring constant: property of a spring determined by a material & number of coils in the spring

    • measured in N/m

    • always the same for a given spring

      • extension/weight

Unit 3 : Energy

energy: ability to do work

    mechanical energy: energy due to motion or the position/shape of an object

kinetic energy: energy of motion

• $KE=\frac12mv^2$

potential energy: stored energy that can become motion later

• $GPE=mgh$

• types of potential energy

  • GPE (gravitational potential energy): stored energy by virtue of position in a gravitational field

  • SPE (spring potential energy): stored energy in a stretched/ compressed elastic surface

    • SPE = 1/2k∆x²

total mechanical energy

• $E=KE+PE$

• sum of all energy in a system

conservation of energy

• energy cannot be created/destroyed

• simply changed from one form to another

• within a closed system, E is always constant

net work & graphing

• calculate work done by finding the area under a curve

  • W = F∆xcos(θ)

• net work: sum of the work done by all the forces acting on an object

  • $W=\sum W=W+W+\cdots$

work-energy theorem

• negative work: energy is being removed from the system

• net work allows us to find overall KE of an object

  • ∑W = ∆KE

  • ∑W = W₁ + W₂ + … + W_i = ∆KE = KE_f - KE_i

    • ∑W = net work

    • ∆KE = change in kinetic energy

Unit 4 : Momentum

momentum: “inertia in motion”

• $p=mv$

      p = momentum ($\operatorname{kg}\cdot\frac{m}{s^2}$)

           m = mass (kg)

           v = velocity (m/s²)

• vector

  • direction of momentum is determined by direction of velocity

law of conservation of momentum: “the total momentum of a closed system is constant”

• momentum is conserved (if no outside forces)

application of C.O.M: collisions

• when 2 objects collide, we can evaluate the resultant change in momentum & velocity of both objects using c.o.m

• $P^{tot,i}=P^{tot,f}$

  for 2 objects = $m^1v^{1,i}+m^{^2}v^{2,i}=m^1v^{1,f}+m^2v^{2,f}$

  • for subscripts, remember

    • each object gets a number

    • i = initial, f = final

    • remember i = before, f = after

inelastic collisions

• total KE = not conserved

• stick together

• $m^1v^{1,i}+m^2v^{2,i}=\left(m^1+m^2\right)v^{f}$

elastic collisions

• total KE = conserved\

• “hit & run”; don’t stick

• $m^1v^{1,i}+m^{^2}v^{2,i}=m^1v^{1,f}+m^2v^{2,f}$

explosions: processes that occur in a system where the object in the system are stuck together somehow initially and then break up into smaller parts

• $v^{i}\left(m^1+m^2\right)=m^1v^{1,f}+m^2v^{2,f}$

• $0=m^1v^{1,f}m^2v^{2,f}$

impulse: change in momentum; implies that velocity is changing _{(acceleration)}

• J = ∆p = F∆t

  • J = impulse

  • ∆p = change in momentum (p_f - p_i)

  • F∆t = force times change in time

Unit 5 : Waves & Light

wave: disturbance that repeats regularly in space & time, transmits energy

• amplitude: maximum displacement of a particle in a wave from it’s equilibrium

• wavelength: distance between any successive identical parts of a wave

• period: amount of time it takes a wave to complete 1 cycle

  • $T=\frac{1}{f}$

  • $T=\frac{\sec}{cyc}$

• frequency: how many cycles happen in 1 second

  • $f=\frac{1}{T}$

  • $f=\frac{cyc}{\sec}$

• wave speed: speed at which a wave crest travels

  • $v=\lambda f$

echo: a sound or series of sounds caused by the reflection of sound waves from a surface back to the listener

electromagnetic waves: waves created by the coupling of oscillating electric & magnetic fields

• can travel through a vacuum

mechanical waves: waves produced by the movement of particles in a medium

• requires a medium to travel through

  transverse wave: particles move perpendicular to direction of wave

  

        longitudinal wave: particles move parallel to the direction of the wave

                compression: area with max density

                rarefaction: area with min density

                equilibrium: undisturbed density

                amplitude: magnitude of density change to equilibrium

speed of light

• $c=3.0\cdot10^8\frac{m}{s}$

• all light in a vacuum travels at the same speed

• nothing can travel faster

light as a wave

• $v=\lambda f$

• $c=\lambda f$

electromagnetic spectrum: range of electromagnetic waves when placed in order of increasing frequency and charge

• radio waves: longest wavelengths, lowest frequencies

• microwaves

• infrared

• visible light

  • lowest frequency/longest wavelength: red light

  • highest frequency/shortest wavelength: violet light

• ultraviolet

• x-rays

• gamma rays: shortest wavelengths, highest frequencies

light waves = light rays

• opaque: materials that do not allow light to pass through

• transparent: allow light to pass through in straight lines

refraction: change in direction of a wave as it crosses the boundary between 2 media

reflection: when a light ray strikes a smooth surface and bounces off

scattering: when light rays are redirecting in many different directions when it encounters particles or irregularities in a medium

• index of refraction (n): how much a substance changes the speed of light therefore bends light

• $n=\frac{c}{v}$

  • n = 1 for a vacuum, 1.33 for water, 2.42 for a diamond (highest)

• incident ray: ray that heads toward boundary

• refracted way: ray that heads away from boundary

• normal line: imaginary line we draw perpendicular to boundary where ray hits

  

• angle of incidence: angle btw incident ray & norm. line

• angle of refraction: angle btw refracted ray & norm. line

  • snell’s law: $n^1\sin\left(\theta^{i}\right)=n^2\sin\left(\theta^{r}\right)$

law of reflection: $\theta^{i}=\theta^{r}$

• specular reflection: reflection off a smooth surface

• diffused reflection: reflection off a rough surface

  • critical angle: incident angle art which the refracted ray moves parallel to the boundary (when $\theta^{r}=90\degree$)

    • angles of incidence > critical angle will reflect

Unit 6 : Electricity

electrostatics: study of electric charges at rest

electric charge: fundamental electric property of atoms which causes attraction/repulsion of electrons & protons

• electron charge: $e^{-}=-1.6\cdot10^{-19}C$

• proton charge: $e^{+}=1.6\cdot10^{-19}C$

electric force: force that one charged object exerts on another

coulomb’s law: electrical forces of 2 charged objects is directly proportional to the product of their charges & inversely proportional to the square of the distance between them

• $F^{e}=k\frac{q^1q^2}{r^2}$

  • $k=9\cdot10^9$

electric field: field force that fills space and every electric charge or group of charges

    all charged objects have a field outside of them

• $F^{e}=E\cdot q$

  • E = magnitude of electric field

  • q = magnitude of charge

electric current: a flow of charge

• flow = amt of charge/time

• $I=\frac{Q}{t}$

  • measured in Amperes (Amps)

electric potential energy: energy stored in an electrically charged object due to its position in an electric field

electric potential difference (voltage): change in potential energy per unit of charge flowing

• voltage is a “push”

• objects always go from high voltage → low voltage

resistance: slowing down of current flow in a material because of the interaction btw the moving electrons and atoms of the wire

• measured in Ohms (Ω)

  factors affecting resistance

  • length of the wire—longer = more resistance

  • width/thickness of the wire—smaller thickness = more resistance

  • material of the wire—more conductive = less resistance

• current is directly proportional to voltage

• current is indirectly proportional to resistance

• $I=\frac{V}{R}$ or $V=IR$

circuit: a closed path made of a conductor which allows electron flow if there’s an energy source

• battery: an energy storage device (provides voltage)

• resistors: provide a given resistance (lightbulbs are glorified resistors)

• ground: literally hooked up to the ground—where charge can be dumped

• switch: controls the flow of current

  • ammeter: measures current

  • voltmeter: measures voltage

series circuit: contains one pathway for electricity to flow

• current is constant around the circuit

parallel circuit: multiple pathways for electricity to flow

• voltage is constant around the circuit

    equivalent resistance: what resistance would be if there was only one big resistor

• for series: $R^{eq}=R^1+R^2+\cdots$

• for parallel: $\frac{1}{R^{eq}}=\frac{1}{R^1}+\frac{1}{R^2}=\ldots$

power in a circuit: $P=IV$

• $P=I\left(IR\right)=I^2R$

• $P=\left(\frac{V}{R}\right)V=\frac{V^2}{R}$