# Physics - Reference Guides

3184 views4 pages
Published on 4 Jun 2015
School
UTEP
Department
Basic Engineering
Course
BE 1101
Professor
MECHANICS
Physics
Physics
permacharts.com
VELOCITY & ACCELERATION
PARTICLE DYNAMICS
Y
X
s
a
v
θ
v
x
v
y
θ
s
r
aR
aT
v
vvv
vdx
dt v
vdy
dt v
xy
x
y
=+ ==
==
22cos
sin
θ
θ
vds
dt rd
dt
==
θ
dt
dt a
dt a
xx
y
y
===
==
cos
sin
θ
θ
vdv
dt dt gt h vdt gt
tt
===
====
∫∫
981
1
2
00
2
.m/s
2
Angular velocity
Note:
a= Constant (e.g., free fall)
Acceleration Velocity Diagrams
Angular
acceleration
Tangential
acceleration
Centripetal
acceleration
a = Constant
αω
=ddt
arddt
T=()
ω
av
r
R=2
ωω α
θω α
=+
=+
t
tt
1
2
2
ωθ
==d dt v r
Rectilinear Motion Circular Motion
ENERGY
Work/Power/Kinetic Energy
Rectilinear Motion Circular Motion
Equilibrium Momentum & Force Inertia
Rectilinear Motion Circular Motion
xxmmxdmdm
yymmydmdm
cm i i i
cm i i i
..
..
=⇒
∫∫
=⇒
∫∫
∑∑
∑∑
Center of Mass (Gravity)
Force (Newton’s Second Law)
Imr rdm
ImR ImR
ii
=⇒
==
22
22
2
5
1
2
Sphere: Cylinder:
Moment of Inertia
Torque
Gravitational Force Centripetal Force
Transitional Equilibrium Rotational Equilibrium
Conservation of linear
momentum
Conservation of angular
momentum
Linear Momentum Angular Momentum
pmv=
LI=
ω
τ
ω
==
==
Fr
dL
dt Id
dt
Force Lever Arm
Fmv
rmr
C==
22
ω
FG
mm
rG
G==
12
2
11
66710.Nm
kg
2
2
Fmv
rmr
C==
22
ω
FFandF
xy
∑∑ ∑
== =000( )
τ
==011 2 2
()Lever Rule:Fr F r
p
F
system
external
=…
=
constant
if 0
L
system
external
=…
=
constant
if
τ
0
WFs=cos
θ
Wmgh=(Potential Energy)
Kmv=1
2
2
PdW
dt Fv= =
WI
d
dt
==
τθ ωθ
PdW
dt
d
dt Id
dt
== =
τθωω
Work (Constant Force)
Work (gravity)
Power (Constant Force)
Kinetic energy
Power (Constant Torque)
Work (Constant Torque)
HARMONIC MOTION
Note: Conservation of
mechanical energy
ﬁ∑K+ U= constant
KI=1
2
2
ω
Kinetic energy
xA t= +sin( )
ωφ
vA t= +
ωωφ
cos( )
aAt=−+
ωωφ
2sin( )
Tv
m
k
== =
12 2
π
ωπ
m
m
m
x = A v = 0 a = – A
2
x = 0 v = A a = 0
x = –A v = 0 a = A
2
ω
ω
ω
Total energy
constant
=
=+=
1
2
2
kA
UK
FkxUFdxkx
Kmv
=− = =
=
1
2
2
1
2
2
ωπν
=2
A= amplitude
f
= phase
angle
U= potential
energy
n
= frequency
K= kinetic
energy
k= spring
constant
m= mass
Displacement
Velocity
Mass On Spring
Acceleration
Period
Angular frequency
FLUID MOTION: CONSTANT RATE & DENSITY
h1
h
A
v
p
2
2
2
2
A
v
p
1
1
1
QvA vA==⇒ =
11 2 2 Flow In Flow Out
pgh vp gh v
pgh v
11
1
21
222
1
22
2
1
2
2
++ =+ +
⇒+ + =
ρρ ρ ρ
ρρ
constant
vgh
22[()]
vv p gh
12
0===
∆∆ρ
Q= flow rate
r
= density
p= pressure = force/area
Continuity Equation
Bernoulli Equation
Torricelli’s Equation
(v1 0)
Hydrostatic Pressure
MAGNETISM
Bi
d
d
=
µ
π
2
(at )
BiNl=
µ
(at axis)
ε
==
W
qBlv
ε
=−Nd AB
dt
()
ε
=−Ldi
dt
System Magnetic Field Produced
Straight wire of length l,
carrying current, i
Coil Nturns, length l,
carrying current i
System EMF Induced
Wire moving in magnetic field
Coil in time varying
magnetic field
Self-induction
L= inductance
(henry, H): 1 H =
1 volt-second/ampere
B = magnetic field
(tesla, T): 1 T = 104
gauss = 1 newton/
ampere-meter =
1 weber/m2:
m°= permeability
MAGNETIC FIELDS PRODUCED BY CURRENTS CURRENTS INDUCED BY MAGNETIC FIELDS
Bernoulli Equation
l e a r n r e f e r e n c e r e v i e w i n s t a n t l y
TM
permacharts
PHYSICS • A-733-11© 2002-2012 Mindsource Technologies Inc.
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