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MECH 2 Dynamics Formula and Data Sheet
Some Standard Physical Constants:
Acceleration at Sea Level due to Gravity:
2
m/s
81
.
9
=
g
.
Speed of light:
m/s
10
3
8
×
=
c
. (Nothing in this course goes that fast, so please check your work if you compute a number anywhere near this!)
Particle Kinematics(Phys 170 Review Material)
Concept
Formulae
Rectilinear (Straight Line) Motion:
This occurs when position,
velocity and acceleration are all along the same direction.
v
ds
dt
a
dv
dt
ads
vdv
==
=
for
constant
acceleration:
()
sa
t
v
t
s
va
tv
vv
a
s
s
c
c
c
=+
+
−
1
2
2
2
00
0
2
0
2
0
Curvilinear (curvedpath) motion
can be described using:
•
Rectangular components
(
fixed
frame of reference).
•
Normal and tangential components
(
instantaneous
frame of
reference
with respect to the path
).
The tangential
component,
u
t
,
is along the path of the particle at the
particular instant in time.
The normal component,
u
n
, is
perpendicular to the tangential component and points
toward the centre of curvature of the path at that point. The
binormal component,
u
b
=
u
t
x
u
n
.
•
Cylindrical (including polar) coordinates
(
instantaneous
frame of reference,
with respect to a fixed origin
).
The
radial component,
u
r
is along the vector from the origin to
the particle.
The transverse component,
u
θ
is along the
direction of increasing angle
θ
with respect to a fixed
reference line.
The third component direction is along the z
axis out of the plane of motion,
u
z
.
rectangular components
:
vxav
vyav
vzav
xx
x
yy
y
zz
z
&&
normal and tangential components:
vu
u
au
u
u
u
uu
=
+
&
&
&
sv
v
dv
ds
v
aa
tt
tn
t n
nn
θ
ρ
2
,
2
2
2
3
2
1
dx
y
d
dx
dy
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
=
cylindrical components:
(
)
ru
u
u
u
u
=
=
+
=−
+
+
r
rr
v
v
r r
r
r
r
&
&
&
&
&
θθ
2
2
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Rigid Body Kinematics
Concept
Formulae
Rotation about a Fixed Axis:
Same equations as rectilinear motion, substituting linear
acceleration (
a
) with angular acceleration (
α
), linear speed,
(
v
) with angular speed (
ω
), and distance, (
s
) with angle (
θ
).
ω
θ
α
αθ ωω
==
=
d
dt
d
dt
dd
for
constant
acceleration:
()
θα
ωθ
ωα
ωω
=+
+
−
1
2
2
2
00
0
2
0
2
0
c
c
c
tt
t
Absolute General Plane Motion:
Describe the position of the point in terms of absolute (
x, y
), (
r,
θ
), or distance (
s
or
θ
) coordinates.
Relate rectilinear and angular position via
trigonometric equations, e.g.
s=f
(
).
Differentiate these equations to get ultimate relationships between
v
and
ω
,
a
and
α
.
Do not make
substitutions of numbers for variables until you have finished differentiating!
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This note was uploaded on 10/26/2010 for the course ENGINEERIN MECH221 taught by Professor Wetton during the Spring '10 term at The University of British Columbia.
 Spring '10
 WETTON
 Dynamics

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