physics equations MCAT

component vectors x and y

X=Vcostheta

Y=Vsin theta

pythagorean theorem

a²+b²=c²

determination of direction from component vectors

angle theta=tan^-1Y/X

Instantaneous velocity

v=lim as t approaches zero deltax/delta t

average velocity

v=deltax/deltat

universal gravitational equation

F_g=Gm₁m₂/r²

static friction

0 ≤f_s ≤ μ_sN

kinetic friction

f_k=μ_kN

force of gravity (weight on earth)

F_g=mg

center of mass

x=(mass object 1)(x coord object1) + (mass ob 2)(x coord object2) +… divided by total mass. Same for y coord

average acceleration

a=delta V/ delta t

Instantaneous acceleration

a= lim as t approaches 0 delta V/ delta t

newton’s first law

F_net= ma= 0

newton’s second law

F_net=ma

newton’s third law

F_AB= -F_BA

kinematics (no displacement)

v=v₀+at

kinematics (no final velocity)

x= v₀t + (at² /2)

Kinematics (no time)

v²= v₀² + 2ax

kinematics (no acceleration)

x=vt

components of gravity on an inclined plane

F_g(parallel)= mg sin theta

F_{g(perpendicular)}=mg cos theta

Centripetal force

F_c=mv²/r

torque

T=r x F= rF sin theta

kinetic energy

K=1/2mv²

gravitational energy

U= mgh

Elastic potential energy

U=1/2kx²

total mechanical energy

E = U + K

Conservation of mechanical energy

ΔE = ΔU + ΔK = 0

work done by nonconservative forces

W_{nonconservative}=ΔE=ΔU + ΔK

definition of mechanical work

W = Fd = Fd cos theta

definition of isobaric gas-piston system work

W = PΔV

definition of power

P = W/t = ΔE/t

Work-energy theorem

W_net= ΔK = K_f - K_i

Mechanical advantage

mechanical advantage = F_out/F_in

Efficiency

Efficiency= W_out/W_in = (load)(load distance)/ (effort)(effort distance)

converting Cel to Fer

F=9/5C + 32

convert Cel to Kelvin

K= C+ 273

thermal expansion

ΔL= alphaLΔT

volume expansion

ΔV = betaVΔT

first law of thermodynamics

ΔU = Q - W

heat gained or lost with temp change

q=mcΔT

heat gained or lost with phase change

q=mL

entropy and heat

ΔS = Q_rev/T

second law of thermodynamics

ΔS_universe= ΔS_system+ ΔS_surroundings > 0

density

p = m/V

weight of a volume of fluid

F_g= pVg

Specific gravity

SG= p/ 1g/cm³

pressure

P=F/A

absolute pressure

P=P₀+ pgz

gauge pressure

P_gauge= P- P_atm= (P₀ + pgz) - P_atm

Pascal’s principle

P= F₁/A₁ = F₂/A₂

Buoyant force

F_buoy= p_fluidV_{fluid displaced}g = p_fluidV_submergedg

Poiseuille’s law

Q= pier^4ΔP/ 8nL

critical speed

v_c= N_Rn/ pD

continuity equation

Q= v₁A₁= v₂A₂

Bernoulli’s equation

P₁+ ½ pv₁² + pgh₁ = P₂ + ½ pv₂² + pgh₂

maximum kinetic energy of an electron in the photoelectric effect

K_max= hv-W

work function

W=hv_T

mass defect and energy

E=mc²

nuclear decay general form