Memorizables 1 Formulas

MCAT Memorizables 1

Net Force

Net Force

Fnet = ma

Fnet= net force

m=mass

a=acceleration

Gravitational Force on Earth

Fg=mg

Fg=gravitational force on earth

m=mass

g=gravitational acceleration

Gravitational Force in General

F_G=Gm₁m₂/r²

^{F_G=Gravitational Force}

^{G=gravitational constant}

^m1,m2=masses

^{r=distance between centers of masses}

Electric Force (charged object into electric field)

F_E=qE

F_E=Electrical Force

q=charge on object

E=electrical field

Electric Force (between two points of charge)

F_E=kq₁q₂/r²

F_E=Electric Force

k=electric force constant

q1,q2=charges on objects

r=distance between the centers of the objects

Electric Field Formula

E=kQ/r²

E=electric field

k=electric force constant

Q=charge

r=distance from charge

Spring Force Formula

F=kx

F=spring force

k=spring constant

x=amount stretched/compressed

(Max) Static Friction Formula

F_s,max=μ_sF_N

F_s,max=max static friction force

μ_s=static friction coefficient

F_N=Normal Force

Kinetic Friction Formula

F_k=μ_kF_N

F_k=Force of Kinetic friction

μ_k=kinetic friction coefficient

F_N=Normal Force

Buoyant Force Formula

F_b=ρVg

F_b=Buoyant Force

V=volume submerged

g=gravitational acceleration

Magnetic Force Formula

F_m=qvBsin(θ)

F_m=Magnetic Force

q=charge

v=velocity

B=strength of magnetic field

θ=angle between direction of velocity and direction of magnetic field

Torque Formula

T=rFsin(θ)

T=Torque (N*m)

r=distance from point that force is applied to pivot point of object rotating about

F=Force causing object to rotate

θ=angle between direction of the force and the line connecting the point the force is acting on to the pivot point of rotation

Net Force on Inclined Plane

F_net=mgsin(θ)

F_net= Net Force

m=mass

g=gravitational acceleration

θ=angle inclined plane makes with ground

Normal Force on Inclined Plane

F_N=mgcos(θ)

F_N=Normal Force

m=mass

g=gravitational acceleration

θ=angle inclined plane makes with ground

Acceleration Formula

a=Δv/t

a=acceleration

Δv=change in velocity

t=time

Simple Distance Formula

d=vt

Three General Motion/Projectile Formulas

1. v_f=v₀+at

2. v_f²=v_0²+2ad

3. d=v₀t+(1/2)at²

Gravitational Acceleration Formula (surface of planet)

g=GM/r²

g=gravitational acceleration (on surface of planet)

G=universal gravitational constant

M=mass of planet

r=radius of planet

Kinetic Energy Formula

KE=1/2mv²

KE - joules (J)

General Work Formula

W=Fdcos(θ)

W=Work

F=Force

d=distance force applied

θ=angle between direction of the force and the direction of the velocity of the object

Net Work Formula

W_net=F_netdcos(θ)

W_net=Net Work

F_net=Net Force

d=distance force applied

θ=angle between direction of the force and the direction of the velocity of the object

Gravitational Potential Energy (close to Earth’s surface)

U_G=mgh

U_G=Gravitational Potential Energy

m=mass

g=gravitational acceleration

h=height of mass

Spring Potential Energy

U_spr=1/2*kx²

U_spr=Spring Potential Energy

k=spring constant

x=amount spring stretched/compressed

Electrical Potential Energy Formula (1 point charge)

U_E=qV

U_E=electrical potential energy

q=charge

V=voltage

Change in Electrical Potential Energy Formula

ΔU_E=qEd

ΔU_E=change in electrical potential energy of object

q=charge

E=strength of constant electrical field

d=distance object “falls”

Change in Voltage formula

ΔV=Ed

ΔV=change in voltage

E=strength of electric field

d=distance the object moves through

Voltage Formula (single point charge)

V=kQ/r

V=voltage

k=electrical constant

Q=charge

r=distance from center of charge

Electrical Potential Energy Formula (2 point charges)

U_E=kq₁q₂/r

U_E=Electrical potential energy

k=electrical constant

q1,q2=charges

r=distance between centers

Energy of Photon Formula

E_p=hf

E_p=energy of photon

h=planck’s constant

f=frequency

Thermal Energy of Friction (kinetic) Formula

E_f= -F_kd

E_f=energy lost by object to heat of friction

F_k=force of kinetic friction

d=distance object travels

General Power Formula (w/o constant velocity)

P=ΔE/t

P=power

ΔE=energy transferred

t=time

General Power Formula 2 (constant velocity)

P=Fv

P=power

F=force

v=velocity

Wave Velocity Formula

v_w=λf

v_w=wave velocity

λ=wavelength

f=frequency

Period of Cycle Formula

T=1/f

T= time period required to complete one cycle

f=frequency

Intensity of Wave Formula 1 (simple)

I=P/A

I=intensity

P=power

A=area

Intensity of Wave Formula 2 (harder one, uses distance)

I₁r₁²=I₂r₂²

I1,I2=intensity at 1,2 location

r1,r2=distance from source at 1,2 location

*inverse square law

Decibels Formula

10log(I/I₀)

I=intensity being studied

I₀=reference intensity which is = to lowest intensity human hears can detect

Beat Frequency Formula

f_beat=f₁-f₂

f_{beat= beat frequency}

f₁=frequency of first wave

f₂=frequency of second wave

*beat frequency produced when two similar frequencies interfere producing 3rd frequency

*cant be negative

General Angular Frequency Formula

ω=2πf

ω=angular frequency

f=regular frequency

Doppler Effect Formula for frequency

f_d=f_s(v_w±v_d)/(v_w±v_s)

f_d=frequency detected

f_s=frequency emitted from source

v_w=velocity of wave

v_d=velocity of detector

Oscillating Spring Angular Frequency Formula

ω=sqrt(k/m)

ω=angular frequency

k=spring constant

Pendulum Angular Frequency Formula

ω=sqrt(g/L)

ω=angular frequency

g=gravitational acceleration

L=length of pendulum

3 General Pressure Formulas

1. P=F/A

2. P_tot=P_atm+P_gauge

3. P_tot=P_atm+ρgh

P=Pressure

F=force

A=area

P_guage=pressure of fluid exerting, pressure on top of atmospheric pressure

ρ=density of liquid

g=gravitational acceleration

h-=height of liquid above point in question (depth)

Specific Gravity of Substance Formula

Specific Gravity = ρ_substance/ρ_water

ρ_{substance=density of substance}

ρ_{water=density of water}

Fraction of Object Submerged Formula

Fraction Submerged = ρ_object/ρ_fluid

Volume Flow Rate Formula

Q=Av

Q=volume flow rate

A=cross sectional area of pipe

v=velocity of fluid

Bernouilli’s Equation

P+1/2ρv²+ρgh = constant

P=pressure

v=velocity

g=gravitational acceleration

h=height

ρ=density of fluid

Surface Tension Formula

T=F/d

T=surface tension

F=force

d=length over which the force is applied

Electrical Current Formula

I=q/t

I=current

q=charge

t=time charge flows

Voltage Drop Formula (ez)

V=IR

Resistance of Resistor Formula

R=ρ(L/A)

R=resistance

ρ=resistivity

L=length of resistor/wire

A=cross sectional area of resistor/wire

Conductivity Formula

σ=1/ρ

σ=conductivity

ρ=resistivity

Equivalent Resistance (In series)

R_eq=R₁+R₂+…

Equivalent Resistance (In parallel)

1/R_eq=1/R₁+1/R₂+…

Charged Stored on Capacitor Formula

Q=CV

Q=charge

C=capacitance (not conductivity)

V=voltage drop across capacitor

Capacitance of parallel plane formula

C=(kE₀A)/d

C=capacitance

k=dielectric constant

E₀=universal electricity constant

A=area of one of capacitor plates

d=distance between plates

Capacitance Circuit (in parallel)

C_eq=C₁+C₂+…

Capacitance Circuit (in series)

1/C_eq=1/C₁+1/C_2^+…

Three formulas for Electrical Power

P_E=IV

P_E=I²R

P_E=V²/R

P_E=Electrical Power

Three formulas for Electrical Energy

U_E=1/2 * Q²/C

U_E=1/2 * CV²

U_E=1/2 * QV

U_E=electrical energy

Q=charge

C=capacitance

V=voltage drop

Average Current formula (AC circuit only)

I_rms=I_max/sqrt2

I_rms=average current

I_{max= max current}

Light passing through medium formula

n=c/v

n_medium=index of refraction of medium

c=speed of light in vacuum (3.0×10^8)

v=speed of light in medium

Two Snell’s Law Formula for Light Passing through Mediums

nsinθ=constant

n₁sinθ₁=n₂sinθ₂

n=respective index of refraction

θ=respective angle the light ray makes with normal line drawn to surface it passes through

Focal Length of spherical mirror formula

f=r/2

f=focal length

r=radius

Focal Length System Formula

1/f=1/d_o+1/d_i

_{f=focal length}

d_o=distance from object to center of lens/mirror

d_i=distance from image to center of lens/mirror

Magnification Formula

m = -d_i/d_o

_{m=magnification (ratio of image height to object height)}

d_i=distance from image to lens/mirror

d_o=distance from object to lens/mirror

*ex: if m=2. image is twice as tall as object

Power of optical system formula

P=1/f

P=power

f=focal length

Thermodynamics: Internal Energy Formula

ΔU=Q+W

ΔU= change in internal energy of substance

Q=heat transferred to gas

W=work performed on gas

Power of Radiation Formula

P_rad=kAT⁴

^{P_rad=power of radiation}

^{k=radiating object constant}

^{T=temperature of radiating object (K)}

^{A=area of object radiating energy}

Total Radiation Formula

Q_rad=kAT⁴t

^{Q_rad=total radiation}

^{k=radiating object constant}

^{T=temperature of radiating object (K)}

^{A=area of object radiating energy}

^t=time

Internal Kinetic Energy of Monatomic Gas Formula

U=3/2*nRT

U=internal kinetic energy

n=number of molecules (moles)

R=gas constant (8.31)

T=temperature (K)