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Table1. Kinematic relations (1D)
Equations of kinematic
Type of Motion
Relationship
General Case
a
*
a z const.
v
Table2. Kinematic relations (2D)
Velocity
Acceleration
Coordinates
Rectangular
(x - y)
dv
dt
ds
dt
*
a const.
v
v0 at
v2
v02 2a s s0
s
s0 vot 1 at 2
2
*
max
Rectangular (x - y)
*
*
6Fy ma y
Normal and
Tangential (n - t)
*
6Fn
*
6Ft
*
6Fr
Polar (r-ș)
*
6FT
*
man
*
mat
*
mar
*
maT
t
vr
an
vt 2
U
vt E
Velocity
vx
vy
UE 2
at vt
ar r rT 2
aT rT 2rT
vT
x
y
vn 0
v UE
t
vr
vT
r
rT
ax x
a y y
an
vt 2
U
vt E
UE 2
at vt
r
rT
* * *
vA vB vA/ B
* * *
vB vA vB/ A
Relative
Motions
ax x
a y y
x
y
vn 0
v UE
Polar (r-ș)
Table3.1 Kinetic relations (Force, Mass, Acceleration)
Equations of
Coordinates
Acceleration
Motion
*
6Fx
vy
Normal and
Tangential
(n - t)
v dv a ds
Special Case
vx
ar r rT 2
aT rT 2rT
*
* *
a A aB a A/ B
*
* *
aB a A aB / A
Table3.2 Kinetic relations (Work and Energy)
Equations of Work and Energy relationship
T1 U12
Annotation
1 mv 2
2
T
T2
* *
dU F ˜ dr
Power : P
dt
dt
* )*
P F ˜V
­ Vg
°
®
° Vg
¯
mgh
1 kx 2 , U c
1 2
2
Ve
* *
F ˜ dr
³1
1 mv 2 , V
g
2
T
T1 Vg ,1 Ve,1 U1c2 T2 Vg ,2 Ve,2
2
U12
mgR 2
, R 6.371(10 )m
r
2 *
*
F
dr
˜
³1
6
* dr*
F˜
dt
Poutput
Pinput
Mechanical efficiency : em
overall efficiency : e em ee et
Table3.3a Kinetic relations (Impulse and Momentum)
Impulse and Momentum (Linear) Impulse and Momentum (Angular)
* *
*
*
6F G
6
M
H
o
o
* t2 *
*
*
*
*
t
2
G1 ³t 6Fdt G2
H
6
M
H
dt
o
o1 ³t
o2
1
1
*
t
*
*
*
* * )* *
)*
mv1 ³t 2 6Fdt mv2
where : H o r u mV , M o r u F
1
Table3.3b Kinetic relations (Impulse and Momentum: Impact)
Direct Central Impact
Oblique Central Impact
m1 v1 n m2 v2
m1v1 m2v2 m1v1c m2v2c
v c vc
e 2 1
v1 v2
e
v2c v1c
n
v1 n v2
m1 v1
m2 v2
t
n
n
n
m1 v1c
t
m1 v1c m2 v2c
n
t
m2 v2c
t
, g 9.81 m / s 2
n