MCAT_Physics Concepts and Equations

component vectors (Chapter 1)

X\=Vcosθ
Y\=Vsinθ

determination of direction from component vectors

θ \= tan

Dot product

A*B \= |A| |B| cosx

cross product

A*B \= |A| |B| sinx

instantaneous velocity

v\=lim (Δx/Δt)
Δt

average velocity

v\=(Δx/Δt)

Universal gravitation equation

Fg \= G m1 m2 / r^2

static friction

0 < fs < usN

kinetic friction

fk\=ukN

Force of gravity equation

Fg\=mg

center of mass

x\= m1x1 + m2x2 + m3x3...../m1 + m2 + m3 + ....

average acceleration

a\=Δv/Δt

instantaneous acceleration

a\= lim (Δv/Δt)
Δt

Newton's First Law

Fnet \=ma \= 0

Newton's Second Law

F\=ma

Newton's Third Law

Fab \=

Kinematics (no displacement)

v \= v0 + at

Kinematics (no final velocity)

x\= v(o)t + (at^2)/2

kinetic energy (chapter 2)

KE \= 1/2mv^2

gravitational potential energy

U \= mgh

elastic potential energy

U \= 1/2kx^2

Total Mechanical Energy

E \= U + K

Conversion of Mechanical Energy

ΔE \= ΔU + ΔK \= 0

Work done by nonconservative forces

Wnonconservative \= ΔE \= ΔU + ΔK

Definition of work (mechanical)

W \= Fd \= Fdcosθ

Definition of work (isobaric gas

piston system)

Definition of power

P \= W/t \= ΔE/t

work

energy theorem

mechanical advantage

Mechanical advantage \= (Fout)/(Fin)

Efficiency

Efficiency \= Wout/Win \= (load)(load Distance)/(effort)(effort distance)

Temperature Conversions (Chapter 3)

F \= 9/5C + 32
K \= C + 273

Thermal expansion equation

ΔL\=αLΔT

Volume expansion equation

ΔV\=βVΔT

first law of thermodynamics

ΔU \= Q

Heat gained or lost (phase change)

Q \= mL

Entropy and heat

ΔS \= Qrev/T

second law of thermodynamics

ΔSuniverse \= ΔSsystem + ΔSsurroundings \> 0

Heat gained or lost (with temperature change)

q \= mcΔT

Density (Chapter 4)

p \= m(mass)/ v (volume)

Weight of a volume of fluid

Fg \= pVg

specfic gravity

sg \= p/ (1 (g/cm3))

pressure

p \= f (force)/ a (area)

Absolute Pressure

P \= Po + pgz

Gauge Pressure

Pgauge \= P

Pascal's Principle

P \= F1/A1 \= F2/A2 F2 \= f1( A2/A1)

buoyant force

Fbuoy \= Pfluid Vfluiddisplaced * g \= Pfluid Vsubmerged *g

Poiseuille's Law

Q\= (πr^4 ∆P)/8ηL

η: viscosity of the fluid
Q: flow rate (volume flowing per time)
ΔP: pressure gradient
r: radius of tube
L: length of tube

Critical Speed

Vc\=(Nr*n)/(p*D)

continuity equation

Q\=v1A1\=v2A2

Bernoulli's Equation

P1 +1/2 ρv_1^2+ρgh_1\= P_2+1/2 ρv_2^2+ρgh_2

P : absolute pressure of the fluid
v: linear speed
h: height of the fluid

Coulomb's Law (chapter 5)

F\=K q₁*q₂/r², magnitude of force between two charges

electric field

E \= (Fe/ q )\= (Kq/r²)

electric potential energy

U \= kQq/r

Electric potential (from electric potential energy)

V \= U /q

Electric potential (from source charge)

V \= kQ/r

Voltage

ΔV \= Vb

Electric potential near a dipole

V \= (kqd/r^2)cosθ

dipole moment

p \= qd

Electric field on the perpendicular bisector of a dipole

E \= (1 / 4πe0) *(p/r^3)

Torque on a dipole in an electric field

T\= p*E*sin(ϴ)

Magnetic field from a straight wire

B \= μ0I/2πr

Magnetic field from a loop of a wire

B\=µ0I/2r

Magnetic force on a moving point charge

Fb \= qvBsinθ

magnetic force on a current carrying wire

Fb\=ILBsinθ

current (chapter 6)

I\=Q/Δt

Kirchoff's Junction Rule

I into junction \= I leaving junction

Kirchoff's Loop Rule

V source \= V drop

Definition of resistance

R \= pL/A

Ohm's Law

V\=IR

Voltage and cell emf

V \= Ecell

Definition of power

P \= W/t \= ΔE/t

electric power

P \= IV \= I^2R \= V^2/R

Voltage drop across circuit elements (series)

Vs\=V1+V2+V3+...+Vn

Equivalent resistance in series

Rs\=R1+R2+R3+...+Rn

Voltage drop across circuit elements (parallel)

Vp\=V1\=V2\=V3\=...\=Vn

Equivalent resistance in parallel

1/Rp \= 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Definition of Capacitance

C\= Q/V

Capacitance based on parallel plate geometry

C\=e0(A/d)

Electric field in a capacitor

E \= V/d

Potential energy of a capacitor

U \= 1/2CV^2

Capacitance with a dielectric material

C' \= kC

Equivalent capacitance (series)

1/Cs \= 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

Equivalent capacitance (parallel)

Cp \= C1 + C2 + C3 + ... + Cn

Wave speed (chapter 7)

v\=fλ

period

T \= 1/f

angular frequency

ω \= 2πf \= 2π/T

speed of sound

v \= √B/p

Doppler effect

f\=f₀(v±Vd)/(v±Vs), Vd is speed of detector, Vs is speed of source. + top

Intensity

I \= P /A

sound level

B \= 10 log (I/Io)

Change in sound level

Bf \= Bi + 10 log (If/Ii)

beat frequency

f\=|f₁

wave length of standing wave (strings and open pipes)

lambda \= 2L /n

Frequency of a standing wave (strings and open pipes)

f \= (nv) / (2L)

Wave length of a standing wave (closed pipes)

lambda \= 4L/n

Frequency of a standing wave (closed pipes)

f \= nv/4L

Speed of light from frequency and wave length (chapter 8)

c \=f*lambda

law of reflection

θ1 \= θ2