PHYS 15200 Formulas and Constants Kinematics

v = v0 +

at

r = r0 +

v0t +12

at2

v2 = v0

2 + 2a(x x0 ) g = 9.81 m/s2 = 32.2 ft/s2

vobj , A =

vobj ,B +vB, A

Uniform Circular Motion

ac = v2 /r = 2r

v =r = 2 /T = 2 f Dynamics p = mv

Fnet = m

a = dp/dt

Fgrav = mg

Fgrav = Gm1m2 /r

2

G = 6.6710-11 N-m2/kg2

Fspring = kx Friction

fk = k N , fs s N Work and Kinetic Energy

W =

F id

W =F ir = Fxcos

Wgrav = mgy

Wspring =

12 k(x2

2 x12 )

K =12 mv

2

Wtotal = K Potential and Total Energy

Ugrav = mgy

Ugrav = GMm/r

Uspring =

12 kx

2

E = K + U =Wnc

F = dU (x)/dx

F =

U

Center of Mass

RCM = mi

ri /M

VCM = mivi /M

ACM = mi

ai /M

M = mi

P = mi

vi

Fext = M

ACM = d

P/dt

Collisions

Impulse =

Fnet dt = p

p =

Favgt

Elastic collisions only:

| v2,i

v1,i |=|v2, f

v1, f | Rotational Kinematics s = R , v = R , atan = R

=0 +t

= 0 +0t +12t

2

2 =0

2 + 2( 0 ) Rotational Dynamics

I points = miri

2 , I = r 2 dm

I parallel = ICM + MD

2

ICM ,rod =

112 ML

2

ICM ,cylinder =

12 MR

2 (solid)

ICM ,cylinder = MR

2 (hollow)

ICM ,sphere =

23 MR

2 (hollow)

ICM ,sphere =

25 MR

2 (solid)

net = I

= r

F , = rF sin

Rotational Energy

Krot =12 ICM

2

Ktrans =12 MVCM

2

Ktotal = Ktrans + Krot

Wrot = d Wrot = Krot

Angular Momentum

L = r p

L = I

Ltotal =

Li

ext = d

Ltotal /dt

Simple Harmonic Motion

d 2xdt2

+ 2x = 0

x(t) = Acos(t + )

= k /m (mass-spring)

= g /L (simple pend)

= /I (torsion pend)

= MgRcm /I (phys pend) Harmonic Waves

2 yx2

1v2

2 yt2

= 0

y(x,t) = Acos(kx t) k = 2 / , = 2 /T v = f = /k

Kmax 2 A2

Waves on a String

v = FT /

= m/L

fn = nv/2L, n = 1,2,3,...

n = 2L/n, n = 1,2,3,... Fluids

P =

FavgA

, = m

V

P2 = P1 + g(h1 h2 )

FB = fluidVdispg

A1v1 = A2v2

P +12 v

2 + gh = const.

water = 1000 kg/m3

Patm = 1.013105 Pa