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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)
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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
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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.)
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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)
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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
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