KINEMATICS OF PARTICLES
UNIFORM RECTILINEAR
a
MOTION
0
v  v0  cons tan t
UNIFORMLY
ACCELERATED MOTION
PROJECTILE MOTION
x  x0  vt
a  cons tan t
v  v 0  at
t2
x  x0  v0 t  a
2
2
2
v  v 0  2a ( x  x 0 )
vX  vX 0
vY  vYO  gt
x  x0  vx 0t
t2
y  y0  v y 0 t  g
2
KINETICS OF PARTICLES: NEWTON'S SECOND LAW


NEWTON'S SECOND LAW
OF MOTION
F  m a


LINEAR MOMENTUM
RATE OF CHANGE OF
ANGULAR MOMENTUM



H  r m v



 MO  H0
WORK AND ENERGY METHODS
Work of a constant force
in rectilinear motion


U12   F  d r
U12  F cosx
U12  Wy =-W(y2-y1)
Work of the weight
Work of the force exerted
by a spring
(x is the deformed distance)
Work of a gravitational
force
U 1 2
U 1 2
1
2
2
 (kx1  kx2 )
2
1 1
 GMm(  )
r2 r1
PRINCIPLE OF WORK AND ENERGY:
T1  U12  T2
CONSERVATION OF ENERGY:
T1  V1  T2  V2
PRINCIPLE OF IMPULSE AND MOMENTUM:
 mv
1
NORMALTANGENTIAL
COORDINATES
RADIALTRANSVERSE
COORDINATES
v x  x v y  y v z  z

a  axi  a y j  az k
a x  x a y  y a z  z

v  vet
 dv
v2
a
et  e n
dt


r  rer

v  rer  re

a  (r  r 2 )er  (r  2r)e

RELATIVE
MOTION
POWER:

v  vxi  v y j  vz k
xB 

 impulse12   mv2
 
P  F v
KINETIC ENERGY
Potential energy of
the weight
Potential energy of a
force exerted by a
spring
Potential energy of a
gravitational force
1
2
1 2
mv
2
V  Wy  mgy
T
V 
1 2
kx
2
V 
GMm
r

 F (t 2  t1 )
Impulse of a constant
force over a finite time
interval
Impulse of a variable
force over a finite time
interval

impulse1 2   F (t )dt
Impulse of an
impulsive force

impulse12  Ft
impulse1 2
t2
t1
OBLIQUE CENTRAL IMPACT
(the velocities are NOT directed along the line of
impact)
Conservation of momentum:
(v A ) t  (v ' A ) t
(v B ) t  (v ' B ) t
m A ( v A ) n  m B ( v B ) n  m A (v ' A ) n  m B (v ' B ) n
CONSERVATION OF MOMENTUM:
 mv   mv

x A x B / A

L  m v
ANGULAR MOMENTUM
RECTANGULAR
COORDINATES
Coefficient of restitution:
(v ' B ) n  (v ' A ) n
e
(v A ) n  (v B ) n
DIRECT CENTRAL IMPACT
(the velocities are directed along the line of impact,
which is normal to the surfaces in contact )
Conservation of momentum:
m A v A  mB v B  m A v ' A  mB v ' B
v'B  v' A
v A  vB
e
Coefficient of restitution:
System of Particles
Newton's Second Law
of motion

Conservation of linear
momentum and
angular momentum

n
 Fi   mi a i
i 1
Sum of moments
 
n 

 r  F i   r  mi a i
Kinetic Energy of
system of Particles
i 1
Linear momentum of a
system of Particles

Mass Center

H o  CONSTANT
T
1 n
mi vi2

2 i 1
T
1
1 n
mtotalvG2   mi vi2/ G
2
2 i 1
L   mi  vi

H0 

n

 r i  mi v i
i 1

n

mtotal r G   mi ri
i 1


F  ma
G
Angular Momentum
about mass center
L =CONSTANT

n
i 1
Angular momentum of
a system of Particles


M

G
T1  U12  T2
Principle of Work and
Energy
Conservation of
Energy
Principle of Impulse
and Momentum
T1  V1  T2  V2


 HG
n 

t2 

L1    F dt  L 2

H G   r i / G  mi v i
t1
i

n 

H G   r i / G  mi v i / G
i
Radius of curvature:

[1  (dy / dx) 2 ]3 / 2
| d 2 y / dx 2 |

t2 

( H 0 )1    M 0 dt ( H 0 ) 2
t1