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Circular Motion
Vocabulary for Circular Motion


Period(T): the time it
takes for one rotation
or revolution.
Measured in seconds.
Rotation: spinning
about an internal
axis, an ice skater
spinning

Revolution:
traveling about an
external axis, kid on
merry-go-round

Centripetal force: a
center-seeking
force, causes
circular motion
Two types of speed to think about:

Linear Speed is total
distance divided by
time. In circular
motion, total distance
is equal to
circumference or 2πr.
The time is equal to
the period.

Rotational speed
(AKA angular speed)
refers to the number
of
rotations/revolutions
per unit of time. A
common unit for this
is RPM. Any guesses
on what RPM stands
for?
Linear Speed

With linear speed, a
point on the outer edge
of an object moves a
greater distance in one
rotation than a point
closer to the center of
the object.
Two ladybugs sit on a rotating
disk, as shown in the figure (the
ladybugs are at rest with
respect to the surface of the
disk and do not slip). Ladybug 1
is halfway between ladybug 2
and the axis of rotation.
A) Which has a great linear
speed?
B) Which has a greater
rotational speed?
Speed/Velocity in a Circle
Consider an object moving in a circle
around a specific origin. The DISTANCE the
object covers in ONE REVOLUTION is
called the CIRCUMFERENCE. The TIME
that it takes to cover this distance is called
the PERIOD.
v
2r
T
Speed is the MAGNITUDE of the
velocity. And while the speed may be
constant, the VELOCITY is NOT. Since
velocity is a vector with BOTH
magnitude AND direction, we see that
the direction, and thus, the velocity, is
ALWAYS changing.
We call this velocity, TANGENTIAL velocity as its
direction is drawn TANGENT to the circle.
CENTRIPETAL FORCE
centripetal force- a center directed force that causes an object to
move in a curved (sometimes circular) path.
Centripetal means "center-seeking" or "toward the center".
It is any force that is at a right angle to the path of a moving object that
has a circular motion.
As you can see by this picture, when on a roller coaster that has a
loop, the passengers experience centripetal force, as well as
inertia.
Centripetal force can be found with the following equations:
Fc = ma= mv2/r= m4π2r/T2
ANALYZING THE FORCES
http://library.thinkquest.org/27948/carousel.html
Centripetal or Centrifugal Force ???
Centripetal and Centrifugal Forces
centrifugal force- an apparent outward force on a rotating or revolving
body. It is fictitious. Due to the fact that our velocity is constantly
tangent to the circular path we are following, a force has to constantly
be pushing/pulling us toward the center. The pressure we feel as a
result of the inward force tricks our minds into thinking we are being
pushed outward.
Video for review
Centrigal Force- NOT http://www.youtube.com/watch?v=Sav9vQ663u4
Centripetal Acceleration
If an object moves in a circle it is accelerating and there has to be an
unbalanced force acting on it. A force that causes circular motion is always
toward the center. Acceleration is always in the same direction as the force
(so centripetal acceleration is toward the center). If, for instance, you tie a
weight on a string and swing it around over your head in a circle you can feel
the centripetal force needed to keep it going in a circle. If you let go, that is
remove the centripetal force, it will fly off in a straight line in whatever direction
it happens to be going at that moment. Centripetal acceleration is found using
the following equations:
ac= v2/r= 4π2r/T2
Drawing the Directions correctly
So for an object traveling in a
counter-clockwise path. The
velocity would be drawn
TANGENT to the circle and the
acceleration would be drawn
TOWARDS the CENTER.
To find the MAGNITUDES of
each we have:
2r
vc 
T
2
v
ac 
r
In what direction will the car continue
if the curve he is about to travel
around is solid ice starting from point
B?
In what direction will the car continue
if the curve he is about to travel
around is solid ice starting half way
between point B and C?
A .013-kg ball is attached to a 0.93-m
string. The ball is swung in a
horizontal circle, making one
revolution in 1.18 s. Find the tension
force exerted by the string on the ball.
What is the direction of the force that
acts on clothes in the washing
machine in the spin cycle?
What is the name and direction of the
force on the ball below?
What is the name and direction of the
acceleration?
Label as Rotating(x) or Revolving(y)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Earth traveling around the sun
Moon traveling around the earth
Earth spinning
Kid on seesaw
Person on roller coaster traveling around a loop
Dog chasing his tail
Ice Skater Spinning
A door
Discus thrower (in reference to the person)
Discus thrower (in reference to the disk)
Book Assignment:
Page 172-173, 49-54