Formula and constants:
Constants:
1 atm 1 01 x 105 N m2; g
9 8 m s2; Density of mercury
Density of sea water 1024 kg m3
13.6x103 kg m3
Moment of Inertia
Parallel axis theorem:
I = Icm + MD2
Center of mass:
Impulse:
; Collision:
Linear Momentum:
Angular Momentum:
=I
=I
; Torque:
: work done: W =
2
kinetic energy of rotation: EK = ½ICM
Solids & Fluids
Fb = mfg = lgVsubmerged
Y
FA
L L0
shear modulus
F A //
G
x L0
p
Fi
Ai
F0
A0
:
Bulk modulus
B
FA
V V0
Oscillations&Waves:
= A cos( t+ )
d2x/dt2
pressure
V V0
p1
Spring-mass system:
k
m
: period (T) = 2 /
Potential energy:(EP) = ½kx2
Kinetic energy: (EK) = ½mv2
Simple pendulum:
g
l
frequency (f) = /2
waves intensity: I = source power/area = Pav/A
spherical waves: I = Pav/4 r2
Level of intensity: = 10 log(I/I0) dB
v vo
Doppler effect: f f
:Mach number = vs/v :
v vs
1
M
v
vs
1
1
2
v12
p2
Damped oscillation:
x(t ) xme bt 2 m cos
k
m
1
2
2
v22
t
b2
4 m2
Standing waves:
both ends are fixed/free: n =2L/n
one fixed-end: n = 4L/(2n-1)
Sound Waves:
speed of sound waves
Y
B
in solids: v
; in fluids: v
in air:
vair (t oC ) 331
273 t
273
331 0.6t
m/s