PHYSICS 1303

PHYSICAL CONSTANTS

m_p = 1.67 ¥ 10^--27 Kg (Proton Mass)

m_e = 9.11 ¥ 10^--31 Kg (Electron Mass)

c = 3 ¥ 10^-8

v = 343 m/s (Speed of Sound in air)

r = 1.21 kg/m³ (density of air)

r = 10³ kg/m³ (density of water)

BASIC FORMULAS

Sphere: A = 4 p r², V= p r³

Cylinder: A = 2 p r L, V= p r² L

A_X = A cos(q); A_Y = A sin(q);

tan(q) = ; A =

VECTOR PRODUCTS

A∑ B= |A| |B| Cos(q) = A_x B_x + A_y B_y + A_z B_z

A¥ B= |A| |B| Sin(q) = x ( A_y B_z - A_z B_y) +

y ( A_z B_x - A_x B_z) +

z ( A_x B_y - A_y B_x)

MECHANICS

x = x₀ + v_0x t + a_x t²

v_x = v_0x + a_x t

2 a_x (Dx) = v- v

y = y₀ + v_0y t + a_y t²

v_y = v_0y + a_y t

2 a_y (Dy) = v- v

= m

F = m a = m

a =

Friction:

f_s ≤ m_s N (Static)

f_K = m_K N (Kinetic)

Work:

W = F • d = F d cosq

F = -kx; W= k x² (Spring)

K = m v²

U = m g h

P = = F • v

1 eV = 1.60 x 10^-19 J

1 hp = 746 W

F(r) =

E_Before = E_After (when E_mechanical is conservered)

System of Particles:

X_CM =

p = mv

F = m a =

J = F Dt = D p

Elastic Collision: (v₁ - v₂) = -(v₁'-v₂')

Inelastic Collision: 0 = -(v₁'-v₂')

QUADRATIC FORMULA

a t² + b t + c = 0

t =

ROTATIONAL MECHANICS

q = q₀ + w₀ t + a t²

w = w₀ + a t

2 a (Dq) = w² - w₀²

= I =

t = I a = r ¥ F = r F sinq = r_^ F

L = I w = r x p = r p sinq = r_^ p

= q

= w =

= a =

K = I w²

I = [b] m r² = S m_i r_i² =

Sphere: b= 2/5

Disk: b=1/2

Hoop: b=1

I = I _CM + M h² (Parallel Axis Theorem)

OSCILLATIONS:

1 Hz = 1 = 2 p Radians = 360 Degrees

T =

w = 2 p f = = = =

x(t) = + x_m Cos( w t + f ) .

v(t) = - v_m Sin( w t + f ) ; v_m = w x_m

a(t) = - a_m Cos( w t + f ) ; a_m = w ² x_m

_{K = m v}²_{; U = k x}²

GRAVITATION:

F = G ; U = - G

G = 6.67 x 10^-11 N-m²/kg²

FLUIDS:

P + r v² + r g h = constant

14.7 lbs/in²= 76 cm-Hg = 760 mm-Hg =

= 760 Torr = 1 atm = 1.01 x 10⁵ Pa

WAVES:

y(x,t) = y_max Sin( k x ± w t)

= k =

= f =

v = = = l f

f_beats = f₁ - f₂

f' = f Doppler