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

download Formula Sheet – Physics   Sheet – Physics 111 Vectors and math Geometry perimeter circle: 2 ... 12 M(L2+W) L a b Rigid-body motion KE= 1 2 Mv CM 2+ 1 2 I CM

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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