is the motion of an object in a circle with a constant or...
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Uniform Circular Motion
is the motion of an object in a circle with a
constant or uniform speed.
What is circular motion?
Anything that
rotates or
revolves around
a central axis is
in circular motion.
Rotation vs. Revolution
Rotation: an object turns about an
internal axis. “Spinning”
Revolution: an object turns about an
external axis, “Turning”
An axis is the straight line around which
rotation takes place.
Rotation vs. Revolution
Where is rotation?
Where is revolving?
As an object moves in a uniform circle
What happens to its speed?
What happens to its velocity?
What happens to its acceleration?
Identify the three controls on an
automobile which allow the car to be
accelerated.
conditions for uniform circular motion
A
V
Miniature golf: where will the golf ball go?
Over point A, B, or C?
A
B
C
B
What causes an object to have
Centripetal Acceleration?
Centripetal Force NOT centrifugal force
What’s the difference?
Centripetal = center seeking
Centrifugal = outward seeking
Without a net centripetal force, an object cannot
travel in circular motion. In fact, if the forces are
balanced, then an object in motion continues in
motion in a straight line at constant speed.
Without a centripetal
force, an object in
motion continues
along a straight-line
path.
With a centripetal
force, an object in
motion will be
accelerated and
change its
direction.
Courtesy http://www.physicsclassroom.com/mmedia/circmot/cf.cfm
frame of reference
Centripetal forces are those seen by an
observer in an inertial frame of reference.
Centrifugal forces are those felt by an
observer in an accelerating frame of
reference. As a car goes around a corner,
the passengers think they feel a force
towards the outside of the curve, in reality
this is due to inertia. Centrifugal force is a
misnomer!!!
What causes centripetal acceleration?
To have acceleration, there must be a net force
towards the center of the circle
What is the force for the following:
Earth circling the sun
Force of Gravity
Car turning a bend
Force of Friction
Xena warrior princess throwing a ball on a chain
Force of Tension on chain
conditions for uniform circular motionSpeed:
constant magnitude
Velocity:
constant magnitude, changing direction tangent
to circle
Velocity vector & acceleration vector:
perpendicular to each other.
Acceleration vector:
directed inwards
changes direction of the velocity vector not the
magnitude
Force vector:
directed inwards
Formulas
Calculating Period and Frequency
ond
srevolutionf
srevolution
ondsT
sec
sec
T = period or time
for one
revolution (sec)
f = frequency or
revolutions per
second (Hz or
sec-1)
Calculating speed
v = speed (m/s)
r = radius of circle
(m)
T = period or time
for one
revolution (sec)
f = frequency
T
rv
2
rfv 2
OR
Formulas
Calculating Centripetal Acceleration
using speed
ac = centripetal
acceleration (m/s2)
r = radius of circle (m)
v = speed (m/s)
av
rc
2
Formulas
Calculating centripetal force using
centripetal acceleration
Fc = centripetal force (N)
m = mass (kg)
ac = centripetal
acceleration (m/s2)
F mac c
r
mvFc
2
OR
Example
A little girl is swinging her 5 kg purse in
horizontal circles using the strap that
allows the purse to swing 20 cm from her
hand. The girl is able to get the purse to
make 10 revolutions in 8 seconds. What
was the speed of the purse? What is the
centripetal acceleration of the purse? How
much tension is in the purse string?
Example
Given:
m = r = T =
Example determine velocity
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
T
rv
2
Example determine velocity
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
sec/57.1
sec/8.0
)2.0(2
2
mv
rev
mv
T
rv
Example determine acceleration with
velocity of 1.57 m/s
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
r
vac
2
Example determine acceleration with
velocity of 1.57 m/s
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
2
2
2
/3.12
2.0
)/57.1(
sma
m
sma
r
va
c
c
c
Example determine FC with
acceleration of 12,3 m/s2
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
maFc
Example determine FC with
acceleration of 12.3 m/s2
Given: m = 5 kg r = 20 cm = 0.2 m
T = (8sec / 10rev) = 0.8 sec/rev
NF
smkgF
maF
c
c
c
5.61
)/3.12)(5( 2
the average speed and the radius of the
circle are ________ proportional.
A twofold increase in radius corresponds
to a _______ increase in speed if period
remains the same
Concept questions:
An object moves in uniform horizontal circular motion. If the radius of the object triples, what happens to the speed of the object?
The speed will triple
How does doubling velocity affect the ac?
It increases four fold
How would calculating Fc change if the uniform circular motion was vertical instead of horizontal?
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