Transcript Circular Motion

CONTENTS
o Angular Velocity and Acceleration
o Centripetal force centrifugal force.
Some illustrations of centrifugal
force.
o Effect on centripetal force on
changing velocity ,mass, radius.
o Motion in a verticle circle
o Relationship between linear and
angular acceleration
o Centripetal acceleration
What is circular motion?
Circular motion is a motion in
a circle at constant speed.
Angular velocity
It is defined as the ratio of angular
displacement to the time taken by
the object to undergo the
displacement.
Angular acceleration
It is defined as the ratio of change
in angular velocity of the object to
the time taken to undergo the
change in angular velocity.
Centripetal force
centrifugal force


An external force required to
make a body move along
circular path with uniform
speed is called centripetal
force.
The outward radial force
experienced by an object
,when in circular motion, is
called centrifugal force
Effect on centripetal
force on changing
velocity
• The smaller the velocity of the
object, the less centripetal force
you will have to apply.
Effect on centripetal force on
changing radius.
• The smaller the length of rope (radius ) the
more centripetal force you will have to
apply to the rope.
SOME ILLUSTRATIONS
OF CENTRIFUGAL
FORCE
CENTRIFUGE:IT IS A DEVICE USED TO SEPARATE LIGHTER
PARTICLES IN SUSPENSION FROM THE MORE DENSE
LIQUID IN WHICH THEY ARE CONTAINED.
Example:
1)Cream is separated from the milk in cream separator.
2)In sugar industries, sugar crystals are separated from the
molasses.
3)The wet clothes are dried by dry cleaners in the drying machines.
4)Centrifuges are used to separate honey from the wax.

MOTION IN A VERTICAL CIRCLE
The motion of a mass on a string in a
verticle circle includes a number of
mechanical concepts.
It must satisfy the constraints of
centripetal force to remain in a circle
,and must satisfy the demands of
conservation of energy as
gravitational potential energy is
converted to kinetic energy when the
mass moves downward.
MOTION IN A VERTICAL
CIRCLE
Consider a body of mass M
tied at the end of a string and  Let us find the minimum velocity the body
whirled in a vertical circle of
should possess at the lowest point in
order to just loop the vertical circle. A/Q to
radius r. let v1 and v2 be
the principle of conservation of energy,
velocities of the body and T
and T be tensions in the string
K.E. of the body at point A =(P.E. +K.E.) of
the body at point B
at the lowest point A and
v
highest point B respectively.
At the lowest point A
T – Mg = Mv2 /r
1
1
 At the highest point B
Mv12  Mg (2r )  Mv22
2
2
T + Mg = Mv2/r
v12  4 gr  v22
 The tension T at the highest
point is zero,
v2  gr , wehave
0 + Mg = Mv2/r
v12  4 gr  gr
V2 = √g r
2
1
v1 
5 gr
SOME ILLUSTRATIONS OF
CENTRIFUGAL FORCE
• CENTRIFUGE:IT IS A DEVICE USED TO
SEPARATE LIGHTER PARTICLES IN SUSPENSION
FROM THE MORE DENSE LIQUID IN WHICH THEY
ARE CONTAINED.
Example:
1)Cream is separated from the milk in cream separator.
2)In sugar industries, sugar crystals are separated from
the molasses.
3)The wet clothes are dried by dry cleaners in the
drying machines.
4)Centrifuges are used to separate honey from the wax.
Centripetal acceleration
The velocity vector at
any point is tangent to
the circular path at that
point , the acceleration
vector acts along the
radius of the circle at
that point and is
directed towards
centre.It is called the
centripetal acceleration.
In this figure , the tire is
spinning which means
a larger centripetal
force is required to
keep the mud in the
circular path of the
tire.
In this figure ,the
“sticky” are adhesive
forces from the mud to
the tire tread are large
enough to be the
centripetal force
required to keep the
mud in a circular path
as the tire spins.
Centripetal Force Calculation
Centripetal force = mass x velocity^2 / radius
Any of the data values may be changed . When
finished with data entry, click on the quantity you
wish to calculate in the formula above. Unit
conversions will be carried out as you enter data ,
but values will not be forced to be consistent until
you click on the desired quantity.
CALCULATION FOR:
Radius = r =
m=
ft
slugs
kg =
Mass = m =
Weight = w =
Nm=
=
lbs
Velocity = v=
m/s =
ft/s
Or in common highway speed units,
mi\h
km/h=
velocity =
Centripetal force = F=
lbs
N=
Calculate
Calculate
AKNOWLEDGEMENT

I AM HIGHLY INDATETD TO OUR
RESPECTED COMPUTER TEACHER,
PHYSICS TEACHER FOR THEIR
CONSTANT GUIDENESS TO MAKE
THIS PROJECT EFFECTIVE ONE.I
EXTENT MY HERTIEST THANKS TO
OUR CLASSMATES FOR THEIR COPERATION.