6. The RReellaattiioonnsshhiipp ooff AAnngguullaarr VVeelloocciittyy
wwiitthh PPeerriioodd aanndd FFrreeqquueennccyy
The Relationship of Angular Velocity
with Linear Velocity
WWhheerree
ωω -- aanngguullaarr vveelloocciittyy ((rraadd//ss))
vv -- lliinneeaarr vveelloocciittyy ((mmss--11))
7. TThhee UUnniiffoorrmm CCiirrccuullaarr MMoottiioonn
AAnngguullaarr DDiissttaannccee oorr DDiisspplleecceemmeenntt
AAnngguullaarr VVeelloocciittyy
AAnngguullaarr AAcccceelleerraattiioonn
0 w =w
q =q +wt 0
0 w =w
w w -
w a
0 0 = 0
D
=
= D
t t
D
8. oTangential Acceleration
a = R = R(0) = 0 t a
o Centripetal Acceleration
o Centripetal force
m R
F m v S
R
2
2
= = w
9. The Wheels Connection
For two wheels that connected on center, thus
the direction of rotation same with the angular
velocity.
2
v 1
=
v
w =w 1 2 or
R
R
1
2
For two wheels that touch connected, thus
the direction two of them is adversative, and
the angular velocity is same
vv11 == vv22 oorr ωω11RR11 == ωω22RR22
For two wheels that connected with string or
chain, thus the direction of rotation and the
linear speed two of them is same
10. Accelerated Uniform Circular Motion
Angular Distance or Displecement
2
q =q +w t + 1 at
0 0 2
If , tthheenn
Angular Velocity
q =w t + 1 at
0 0 q = 2
0 2
w =w +at 0
Angular Accelaration
a =
a 2 + a
2
s t WWhheerree
aa -- ttoottaall aacccceelleerraattiioonn ((mm//ss22))
23. CCeennttrriippeettaall aacccceelleerraattiioonn
&& lliinneeaarr vveelloocciittyy
1. The centripetal force
produces an
acceleration towards
the centre.
2. This acceleration is
changing the direction
of the linear velocity,
so as to keep the
object in the circle.