Physics-Equations version 5 Updated for Use PDF

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Common Physics Equations Motion 𝒗𝒂𝒗𝒆

𝒗𝒂𝒗𝒆

𝒂=

=

Variables: (mks unit)

𝜟𝒙 = 𝒕

vave : average velocity (m/s) Δx or x : change in position or displacement (m)

(𝒗𝒊 + 𝒗𝒇 )

Δt or t : change in time or time (s)

𝒕

𝜟𝒗 (𝒗𝒇 − 𝒗𝒊 ) = 𝒕 𝒕

Δv : change in velocity (m/s) vi : initial velocity (m/s)

𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕

vf : final velocity (m/s) a : acceleration (m/s2)

𝒗𝟐𝒇 = 𝒗𝒊𝟐 + 𝟐𝒂𝜟𝒙

𝜟𝒙 = 𝒗𝒊 𝒕 + 𝟏/𝟐 𝒂𝒕𝟐 𝒙 = (

𝒗𝒊 + 𝒗𝒇 )𝒕 𝟐

(note: on many different equation sheets x is substituted by d for displacement)

Projectile Motion X axis projectile equation 𝒙 = 𝒗𝒙 𝒕

Note: the Y axis equations are the same as the accelerated motion equations above but specialized for something in freefall along the Y axis

Variables (mks unit)

Y axis projectile equations 𝜟𝒚 = 𝒗𝒊𝒚𝒕 + 𝟏/𝟐 𝒈𝒕𝟐 𝒗𝒇𝒚 = 𝒗𝒊𝒚 + 𝒈𝒕

𝟐 𝒗𝒇𝒚

=

𝟐 𝒗𝒊𝒚

+ 𝟐𝒈𝜟𝒚

𝒈 = 𝟗. 𝟖 𝒎/𝒔𝟐

Only if viy = 0 𝜟𝒚 = 𝒗𝒊𝒚𝒕 + 𝟏/𝟐 𝒈𝒕𝟐 Becomes 𝒕 = √(

𝟐𝜟𝒚 ) 𝒈

Δy or y : change in position or displacement (m) in the y axis Δv : change in velocity (m/s) Viy : initial Y axis velocity (m/s) Vfy : final Y axis velocity (m/s) g : acceleration due to gravity (m/s2)

Variables (mks unit)

Force and Friction ∑ 𝑭 = 𝑭𝒏𝒆𝒕 = 𝒎𝒂 m1a1 = m2a2

∑ 𝑭 𝒐𝒓 𝑭𝒏𝒆𝒕 ∶ 𝒗𝒆𝒄𝒕𝒐𝒓 𝒔𝒖𝒎 𝒐𝒇 𝒇𝒐𝒓𝒄𝒆𝒔 (𝑵) m : mass (kg)

𝑭𝑾 = 𝒎𝒈

a : acceleration (m/s2)

𝑭𝒔 = −𝒌𝒙

Ff : Force of friction (N)

𝑭𝒇 = µ𝑭𝑵

FW : weight (N)

µ : coefficient of friction (no unit) Fs : Spring Force (N) k : spring constant (N/m or kg/s2) x: displacement of stretched spring (m)

Gravitation and Circular Motion 𝑭𝒄 = 𝒎𝒂𝒄

Fc : centripetal force (N)

𝒎𝒗𝟐 𝑭𝒄 = 𝒓 𝒂𝒄 =

ac : centripetal acceleration (m/s2) v : velocity (m/s)

𝒗𝟐 𝒓

r : radius (m)

𝟐𝝅𝒓 𝒗= 𝑻

𝑭𝒈 =

𝑮𝒎𝟏𝒎𝟐 𝒅𝟐

𝑮 = 𝟔. 𝟔𝟕𝒙𝟏𝟎−𝟏𝟏 Ƭ = 𝑭⟘ 𝒅

𝑭𝟏 𝒅𝟏 = 𝑭𝟐 𝒅𝟐 𝒇=

𝟏 𝑻

𝟏 𝑻= 𝒇

Variables (mks unit)

π : pie (3.14 rounded) Fg : Force of Gravity (N) 𝑵𝒎𝟐

𝑵𝒎𝟐 𝒌𝒈𝟐

G : universal gravitation constant ( 𝒌𝒈𝟐 ) m1 : mass one (kg) m2 : mass two (kg) d : distance between objects (m) Ƭ : Torque (Nm) F⟘: Pe Perp rp rpen en endi di dicular cular Fo Forrce ((N N) T: Period (s) f: Frequency (Hz) F1 and F2 represent two different forces created by object 1 or 2 (N) d1 and d2 represent two different distances that object one or two are from the fulcrum or rotational point (m)

Energy and Momentum

Variables (mks unit)

PE = mgh

PE : potential energy (J)

KE = ½ mv2

m : mass (kg)

PEi + KEi = PEf + KEf

g : acceleration due to gravity (m/s2)

mghi + ½ mvi2 = mghf + ½ mvf2

h : height (m)

P = mv

KE : kinetic energy (J)

Impulse = FΔt

v : velocity (m/s)

FΔt = Δ(mv)

p : momentum (kg∙m/s) J: Impulse (Ns)

Elastic Collisions

m1 : first objects mass (kg)

m1v1i + m2v2i = m1v1f+m2v2f

v1i : first objects initial velocity (m/s) m2 : second mass (kg) v2i : second objects initial velocity (m/s) v1f : first objects final velocity (m/s) v2f : second object final velocity (m/s) vf : combined final velocity (m/s)

Work and Power

Variables (mks unit)

W = F// d

W : work (J)

𝑷=

𝑷=

𝑾 𝒕

P : power (W)

𝑭//𝒅

F// : Force parallel to the motion (N)

𝒕

W = ΔKE

Simple Machines

Variables (mks unit)

𝑰𝑴𝑨 =

IMA : Ideal Mechanical Advantage (none)

𝑨𝑴𝑨 =

𝒅𝒊𝒏 𝒅𝒐𝒖𝒕

𝑭𝒐𝒖𝒕 𝑭𝒊𝒏

𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 =

din : distance on input side (m) dout : distance on output side (m) 𝑾𝒐𝒖𝒕 𝑾𝒊𝒏

X 100%

Fin : Force on input side (N) Fout : Force on output side (N) Fout is force provided by the machine and equal to the weight you are trying to lift

Variables (mks unit)

Electricity 𝑭 𝒆𝒍

𝒌𝒒𝟏𝒒𝟐 = 𝒅𝟐

Fel : electrical force (N)

𝑵𝒎 𝒌 = 𝟗. 𝟎𝒙𝟏𝟎 𝑪𝟐 𝒒 𝑰 = V = IR 𝒕 𝟗

𝑭 𝑬 = 𝒒

𝑬 =

𝑽 𝒅

𝑾 𝑽 = 𝒒

𝟐

P = IV

P = I2R

𝑽𝟐 𝑷 = 𝑹 𝑷 =

𝑬𝒏𝒆𝒓𝒈𝒚 𝒕

qe : charge of electron = -1.6 x 10-19 C

k : coulomb constant (

𝑵𝒎𝟐

q : charge (C)

𝑪𝟐

)

q1 or q2 : multiple objects with charge (C) d : distance between (m) I : current (A) T: time (s) E : electrical field (N/C) V : potential difference or voltage (V) W : work (J) P : power (W) R : resistance (Ω or Ohms)

Series Circuit

𝑽𝒆𝒎𝒇 = 𝒗𝟏 + 𝒗𝟐 + 𝒗𝟑 + ⋯

𝑰𝑻 = 𝑰𝟏 = 𝑰𝟐 = 𝑰𝟑 = ⋯

𝑹𝑻 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + ⋯

Parallel Circuit

𝑽𝒆𝒎𝒇 = 𝒗𝟏 = 𝒗𝟐 = 𝒗𝟑 = ⋯

𝑰𝑻 + 𝑰𝟏 + 𝑰𝟐 + 𝑰𝟑 + ⋯

Variables and Subscripts Subscripts (1,2,3, …): first, second, third resistor or device, and so forth…

T or emf: equivalent or total calculated at the battery or power source

𝟏 𝟏 𝟏 𝟏 + + = +⋯ 𝑹𝑻 𝑹𝟏 𝑹𝟐 𝑹𝟑

V : voltage (m/s)

At Device (more in last section)

R : resistance (Ω or Ohms)

𝑽 = 𝑰𝑹 𝑷 = 𝑰𝑽

I : Current (A)

Variables (mks unit)

Sound and Waves 𝒗 = 𝒇𝝀 𝑻=

v : velocity (m/s)

𝟏 𝒇

f : frequency (Hz)

𝜆 : wavelength (m)

𝟏 𝒇= 𝑻

T : period (s)

Vsound : velocity of sound (m/s)

vsound= 331m/s + 0.6T(°C)

Optics

Variables (mks unit)

𝟏 𝟏 𝟏 = + 𝒇 𝒅𝒊 𝒅𝒐

𝑴=

f : focal length (m) di : distance to image (m)

𝒉𝒊 −𝒅𝒊 = 𝒅𝒐 𝒉𝒐

do : distance to object (m) M : magnification (times)

nisinӨi = nrsinӨr

𝒏𝒓 𝑺𝒊𝒏Ө𝒄 = 𝒏𝒊 𝒏=

hi : height of image (m) ho : height of object (m)

𝒄

𝒗𝒎𝒂𝒕𝒆𝒓𝒊𝒂𝒍

n : index of refraction (no unit) ni : index of refraction incident side (no unit)

c = 3x108 m/s

nr : index of refraction refracted side (no unit) Өi : angle of incidence (°) Өr : angle of refraction (°) Өc : critical angle (°) vmaterial : velocity of light in a material (m/s) c : speed of light or any electromagnetic wave in a vacuum (3x108 m/s)

Trig Reminders 𝒄𝟐 = 𝒂𝟐 + 𝒃𝟐

𝒔𝒊𝒏Ө =

𝒐𝒑𝒑

𝒉𝒚𝒑

𝒄𝒐𝒔Ө =

𝒂𝒅𝒋

𝒉𝒚𝒑

𝒕𝒂𝒏Ө =

𝒐𝒑𝒑 𝒂𝒅𝒋...