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### Transcript of Formula Sheet – Physics Sheet – Physics 111 Vectors and math Geometry perimeter circle: 2 ......

• Formula Sheet Physics 111

Vectors and math

Geometry perimeter circle: 2 R

2area circle: R

2area sphere: 4 R34volume sphere:

3R

1 revolution = 2 radians = 360 o

General kinematics

v =

x2 x1t2 t1

= xt

a =v2 v1t2 t1

= vt

22 40

2b b acax bx c x

a + + = =

!V =V = Vx

2 +Vy2 Vx =V cos

tan =VyVx

Vy =V sin

Conversion factors (for barbaric units) 1 yard = 3 foot = 36 inches 1 inch = 2.54 cm 1 mile = 1.609 km 1 lb = 4.448 N1 gallon = 3.788 liters

Physical constants

g = 9.81 m/s2 11 2 26.67 10 Nm /kgG =

1015 femto- (f)

1012 pico- (p)

109 nano- (n)

106 micro- ()

103 milli- (m)

102 centi- (c)

103 kilo- (k)

106 mega- (M)

109 giga- (G)

1012 tera- (T)

31 m 1000 liters=

1 atm = 1.013105 Pa = 760 mm Hg 1 cal = 4.186 J 1 Cal = 1000 cal

R = 8.314 J

mol K

sound 343 m/s=v

( )8 2 45.67 10 W m K = 23A

1.38 10 J/K= = RkN

NA = 6.0221023 mol1

One-dimensional motion with constant acceleration

x = x0 + v0t +

12

at2 v = v0 + at v2 v0

2 = 2a x x0( ) v =

v+v02

v = lim

t0

xt

a = limt0

vt

( ) tvvxx oo ++= 21

• Two-dimensional motion with constant acceleration

x = x0 + v0xt +

12

axt2

vx = v0x + axt vx2 v0x

2 = 2ax x x0( ) vx =

vx + v0x2

y = y0 + v0 yt +

12

ayt2

vy = v0 y + ayt

vy2 v0 y

2 = 2ay y y0( ) vy =

vy + v0 y2

Projectile motion

x = x0 + vxt vx = constant

y = y0 + v0 yt

12

gt2 vy = v0 y gt

vy2 v0 y

2 = 2g y y0( ) vy =vy + v0 y

2

Forces

!F = m!a

!FG (

!W ) = m!g

Ffr = k FN Ffr sFN

FS = kx

!FAB =

!FBA

FG = G

m1m2r 2

Relative motion

!rA relative to C =

!rA relative to B +!rB relative to C

!vA relative to C =

!vA relative to B +

!vB relative to C

!aA relative to C =

!aA relative to B +!aB relative to C

!rA relative to B =

!rB relative to A

!vA relative to B =

!vB relative to A

!aA relative to B =

!aB relative to A

Circular motion

=

t =

t s = r

Constant : T = 1

f= 2

aC =v2

r= r 2

20 0

12

t t = + + 0 t = + 2 0

2 = 2Constant :"

a = aC2 + atan

2

vtan = r atan = r

=

+02

y = yo + 12 voy + vy( ) t

x = xo + 12 vox + vx( ) t

• Work and energy

PEgrav = mgy

PEelastic =

12

kx2

W = Fd cos Wnet = KE =

12

mv f2 1

2mv0

22

212 2v= = pKE m

m

P = W

t E = KE + PE E = KE + PE =Wnon-conservative

Momentum, impulse. Systems of particles.

!p = m!v

!F =

!pt

!rCM =m!r( )m

!vCM =m!v( )m

!aCM =m!a( )m

When

!Fnet, external = 0,

!ptotal,i =!ptotal,f( )

!Fnet, external =

!ptotalt

= mtotal!aCM

!ptotal =!p = m!v( ) = mtotal!vCM

Isolid sphere =

25

MR2

Ihollow sphere =

23

MR2 Isolid cylinder =

12

MR2 Ihollow cylinder =

12

M R12 + R2

2( )

Irod =

112

ML2 Irectangle =

112

M L2 +W 2( )L " a"

b"

Rigid-body motion

KE = 1

2MvCM

2 + 12

ICM2

KE = 1

2I 2

= Lt

I = mr 2

= rF sin = rF = rF

(For rotation about a fixed axis:

= I and L = I )

Wconservative = PE

elastic collision in one dimension: v1,i v2,i = v1,f v2,f( )( )

L = rpsin = r p = rp

• Gravitation

!F = G

m1m2r 2

g = GmErE

2 circular orbitv =GMr

T 2

r3= 4

2

GM

g = 9.80 m/s2 11 2 26.67 10 Nm /kgG =

ME = 5.981024 kg 6E 6.38 10 m= R

P = P0 + gh

Fluids FPA

= = m

V Av = constant

P + 1

2v2 + gy = constant

Simple harmonic motion

1 2Tf

= =

x = Acos(t)

km

= T = 2 L

g

v = A sin(t) = vmax sin(t) a = A 2 cos(t) = amax cos(t)

I = P

4r 212 2

00

(10 dB) log 1.0 10 W/mI II

= =

Sound

beat a bf f f= fobs =

v sound vobsv sound v source

fsource sound 343 m/sv =

PEgrav = G

Mmr

Mechanical waves

v = f v =

FTm / L

2 f = 1fT

= I = P

4r 2

fn =

vn

= n v2L

n = 1,2,3,... fn =

vn

= n v4L

n = 1,3,5,7...

d1 d2 = n n = 0,1,2,3,... d1 d2 = n+

12

n = 0,1,2,3,...

• Ideal gas

R = 8.314 J

mol K23

A

1.38 10 J/K= = RkN

NA = 6.0221023 mol1 PV = nRT = NkT

n = N

NA

KE = 1

2mv2 = 3

2kRT

v rms =

3kTm

U = 32

nRT (monatomic gas)

= U Q W

Thermodynamics

W = PV

e = W

QH= 1

QLQH

COPrefrigerator =QLW

COPheat pump =QHW

eideal = 1TLTH

S = Q

T S > 0

W = nRT lnVfVi

TF =

95

TC +32 F

Temperature and heat

K 273.15 KCT T= + 0L L T =

Q mc T= Q = mL

Qt= kA

TH TCl ( )8 2 45.67 10 W m K =

Qt

= Ae Tobject4 Tsurrounding

4( )

V = V0T