8/3/2019 PhysFormulas

1/5

PHYSICS 1441 FORMULAS PAGE 1 OF 5 HENRY SCHREINERIII DECEMBER13, 2006

SI units:

Nkgm

s2

=J

m(Newton) -force

Jkg m

2

s2 =Nm (Joule) - energy

Pakg

s2m

=N

m2 (Pascal) -pressure

W kg m

2

s=

J

s(Watt) -power

Hz=1

s (Hertz) -frequency

k=kg

s2

=N

m(spring constant)

Constants:

M=5.981024 kg (mass of earth)

G=6.6731011Nm

2

kg2

R=6.37106 m (radius of earth)

c=2.998108m

s(speed of light)

Constant acceleration formulas:v =v0at ( x )

x=v0t1

2at

2( v )

v2=v0

22 a x ( t )

x=1

2 v0v t ( a )

x=v t1

2at

2( v0 )

Force:

FdU

ds(derivative definition of force)

Wweight =mg=Fg g GMR2 (on earth)Wweight =

GMm

Rh2(h = height above surface)

Fskx (Hook's law)

f FN (friction)

F=f gVf=mg (buoyancy)

PF

A (pressure) (A = area)

stressF

A strain

LL0

(L0 = orig. length)

modulusstress

strain=

FL0

A L(Young's, for L)

L=FL0

Amodulus

Fv=bv (viscosity)

Fd=cv2

(drag)

Energy:

1

1v

c 2

(for v 0.1 c , 1 )

Emc2 (for v 0.1c , E=mc2 )

K=1

2mv

2(v well less than c)

Ugravity=mgh (ifh < 6400 m)Ug

GMmr

(gravity with any two objects)

Us1

2kx

2(spring)

ETOTKU ( and restE, too)

ETOT=0 (conservation of energy)

ve= 2 GMR 12=

2 GM

R(escape velocity)

Work:

WFx x

W=U=K (only if energy is conserved)

Wnc=ETOT (non-conserved work)

Wnc=fx (work by friction)

PdE

dt

E

t(power)

(gravitational constant)

8/3/2019 PhysFormulas

2/5

PHYSICS 1441 FORMULAS PAGE 2 OF 5 HENRY SCHREINERIII DECEMBER13, 2006

Momentum:

pmv (for v 0.1c , p=mv )P pi (sum of momentums) F F

1 F

2 (sum of all forces)

F=d Pdt

P

t(Pis power)

F=m a (Newton's second law)

m v i F t=m v f (basis for impulse)

Impulse F t=J (Jis not Joule)

mv i= mv f (conservation of momentum)

Vectors:

Ax=AcosAy=Asin

A=Ax2Ay2

tan =Ay

Axalso = tan

1AyAx A=Ax iAy jAz k

Dot product: (scalar)

ABAB cos ( = or2 )AB=BAA BC= ABCii=1, ij=0AB=Ax BxAy ByAz Bz

Cross product:

A BABsin n ( )A B=BA

ii=0, ij= kA BC=A BAB

d

dt AB=

d Adt

BAd Bdt

Two Dimensional Motion:

r=x iy jr= r2 r1

v=vx ivy j

a=ax iay j

Projectile motion:

y=x tan 0g x

2

2v0 cos02

y=y0vy 0t 1

2g t

2

y=v0sin 0t 1

2g t

2

vy2=v0 sin 0

22gy

R=v0

2

gsin2 0 (range)

h=v0

2sin2

2g(height)

Basic Circular Motion:

21

s

r(radians - a pure number) (s = arc length)

ds

dtr

ddt

ddt

t( is angular velocity)

d

dt

t( is angular acceleration)

s= r , v = r , a t= r

arv2

r=2r (directed inward)

T2 r

v=

2

(Tis the period of revolution)

For UCM, sub in UAM: x=, v=, a=

Ax

AyA

8/3/2019 PhysFormulas

3/5

PHYSICS 1441 FORMULAS PAGE 3 OF 5 HENRY SCHREINERIII DECEMBER13, 2006

More Circular Motion:

K=Ki=1

2 mi ri22 (kinetic energy)

I mi ri2 (inertia as a sum)

K=1

2I2 (kinetic energy with inertia)

Io=Icmk2

(parallel axis therom)

r F (torque - units: J)

=dLdt

=r Ft=r F=r F sin

net=I (Newton's second law)

r

p (angular momentum)

L= L=I

v=GM

r(orbital velocity)

T2= 4 GMr3 (Kepler's third law)

W=i

f d (work)

W= (for const. torque)

P=dW

dt=

ddt

= (power)

Common Inertia Formulas: (pg. 253)

I=1

2mr

2(cylinder or disk)

I=mr2 (hoop)

I=1

2mR2r2 (ring - shell )

I= 112

ml2

(thin rod)

I=1

4mr

21

12ml

2(thick rod)

I=2

5mr

2(sphere)

I=2

3mr

2(hollow sphere)

Harmonic Motion:

T1

f(period)

x t

disp.

=xmamp.

cos ang.freq.

ttime

phaseangle

phase

(displacement)

v t=xm sin t (angular velocity)

a t=2xm sint

a t=2x t (angular acceleration)

vM=A (max velocity)

aM=2A (max acceleration)

2

T

=2 f (angular frequency)

=k

m(angular frequency) (k= spring const.)

T=2m

k(period)

Ut=1

2k xm

2cos

2 t (potential energy)

Kt=1

2k xm

2sin

2 t (kinetic energy)

Et=1

2 k xm2

(total energy)

Pendulum motion:

Lmgsin =I (actual)

=mgL

I (small angle approx., 0.1)

T=2 L

g(simple pendulum, small ampl.)

T=2

I

mgh (physical pendulum, small ampl.)

8/3/2019 PhysFormulas

4/5

Negative travels forward

PHYSICS 1441 FORMULAS PAGE 4 OF 5 HENRY SCHREINERIII DECEMBER13, 2006

Waves and Sound:

y x , t disp.

=ymamp.

sin kang.

wave

xpos.

ang.freq.

t

time

phase

(disp.)

k2

(angular wave number) (=wavelength)

2

T(angular frequency)

f1

T=

2(frequency)

v=k

=T

= f (wave speed)

=

m

l (linear density of string)

v=

(speed, string) ( = string tension)

Pave=1

2 v 2 ym

2(average power, string)

v=P

(speed, solid) (P=pressure or modulus)

v=R T (speed, gas) (=adiabatic c. mole/kg)

E=

1

2 k A

2

(wave energy)

I=P

A(intensity) A=4 r2

I=1

2 v 2sm

2(intensity) (sm = disp. amplitude)

Standing Waves:

y=2A sin k x

amplitude

cos t

oscillatingterm

(standing wave)

f= v

= n v2L

, forn=1,2,3, . .. . (same ends)

f=v

=

n v

4L, forn=1,3,5, . . .. (odd ends)

Gases:

R8.31J

molK(universal gas constant)

NA

6.0210231

mol (Avogadro's number)

kBR

NA=1.381023

J

K(Boltzmann constant)

n=N

NA

(moles) (N= number of molecules)

n=Msam

M=

Msam

m NA(m = mass of one molecule)

KE=3

2kB T (Kinetic energy of molecules)

v rms=3R T

M=

3 kB T

m(root-mean-square)

pV=nRT (ideal gas law, moles)pV=NkT (ideal gas law, molecules)

L=L0 T (linear expansion) (=cte, in C-1)

Heat and Thermal Power:

CQ

T=

EintT

(C= heat capacity, inJ

K)

c Cm(c = specific heat, in J

kg K)

Q=C T=mc T (relation of heat to temp.)

LQ

m(L = latent heat, for changing phase)

P=Q

t(P= thermal power) (AkaH)

Pcond=k A TL

(k= conductivity, inW

K m)

Pconv=h A T (h = conv. coef., inW

K m2 )

Prad= AT4

(=EM wave radiation eff.)

Pabs= ATenv4

(absorbing rad) (Tenv uniform)

Pnet= ATenv4 T4 (positive if absorbing)

=5.67108W

K4m

2 (Stefan-Boltzmann const.)

(M= molar mass)

(Msam

= mass in sample)

(Q = heat)

8/3/2019 PhysFormulas

5/5

PHYSICS 1441 FORMULAS PAGE 5 OF 5 HENRY SCHREINERIII DECEMBER13, 2006

Thermodynamics:

Q=EintW (first law of thermodynamics)

W=P V (isobaric work) (const. pressure)

W=n RTlnV

i

Vf(isothermal work)

W=0 (isovolumetric work) (const. volume)Q=0=W (isolated system)

Eint=0 (cyclic process)

Q=0 (adiabatic) (const. heat)

PV=constant (isothermal)

PV=constant (adiabatic) (steeper)

=5

3(monatomic)

=7

3(diatomic)

Thermodynamics, cyclic processes, Eint=0 :Q h=QcW (second law of thermodynamics)

eW

Qh=1

Qc

Qh(heat engine) (efficiency)

ec=1

Tc

Th(max eff.) (Carnot eff.)

COP=Qh

W=

Q h

Qh

Qc

=1

e(coef. of performance)

S=Q

T(in

J

K) (entropy)

S=Q

T(isothermal entropy change)

S=0 (reversible) (not common)

S=Qout

Tout

Q

Tin(non-isothermal)

Conversions:

1atm=101.3kPa=14.7lb

in2 (pressure)

1000L=1m3 (volume)

1cal=4.186J (heat) (heats 1g water 1C)1Cal=1kcal=1000 cal (heats 1kg water 1C)TC=T 273.15 (temp K to C)

TF=9

5TC32 (temp C to F)

1mol=6.021023elem.units

1 u=1.671027 kg (atomic unit)

1inch=0.0254 m (English to metric)1yd=0.914 m

1mile=1609m1lb 0.450 kg (atg= 9.81 m/s2)

Lab Formulas:

z=z xx

2

yy 2

% error=xknownxexp

xknown100%

% difference= x

1, expx

2, exp

x1, expx2, exp2 100%

=

N(standard error)

x=1

Ni=1N

x ix (population SD)

sx=1

N1

i=1

N

xix

(standard SD)

vair331.50.607 TC (speed of sound in air)

Isovolumetric

Isobaric

Isothermal

Adiabatic

p

v

(COP = SEER)

(0