Download Circular Motion

The Properties
circumference
diameter
radius
Circumference = 2*pi*Radius
Uniform circular motion
 is the motion of an object in
 a circle
 a constant or uniform speed.
 An object moving in uniform circular
motion would cover the same linear
distance in each second of time
Average Speed
Circumference = 2*pi*Radius
T is the time to make one
cycle around the circle
(period).
R represents the radius of the circle and T represents the period
Example
 On August 24, 1968, a very fast horse named
Dr. Fager finished a race in 1 minute. Assuming
he ran twice around a 10 meter radius circular
track, what was his average speed?
 Solution
 The circumference is 2πR
= 62.8 meters
 The period = time/2 (as he ran twice) = 30 seconds
 The average speed = circumference/period =2.09 m/s
How are speed and radius related?
"  has a constant speed. But does
this mean that it will have a
constant velocity?
"  Speed is a scalar quantity
"  velocity is a vector quantity
An object is moving in a clockwise direction around a
circle at constant speed.
Draw vectors which represent
the direction of the velocity
when the object is located at
points A, B and C on the circle
Acceleration
As the object rounds the circle, the direction
of the velocity vector is different than it was
the instant before
Acceleration
 Because the velocity is not constant,
the object must be accelerating
 Centripetal acceleration or
 Radial acceleration
The Magnitude of Centripetal
Acceleration
R represents the radius of the circle
and V represents the speed
Centripetal Equations
Problems
 
What is the centripetal acceleration of
a child 4.0 m from the center of a
merry-go-round? The child’s speed is
1.1 m/s.
= (1.1m/s)2 / 4m = 0.30 m/s2
Problems
 
 
What is the centripetal acceleration of
a child 4.0 m from the center of a
merry-go-round? The child’s speed is
1.1 m/s.
What is the magnitude of the
acceleration of a spec of dust on the
edge of 20 rpm (revolution per
minute) phonograph record whose
diameter is 30 cm?
and
so a =
20 rpm means 20 revolutions in 1 min
60 sec/20 rev = 3 sec/1 rev, so T = 3 sec
so T = 3 sec
Also, diameter = 30 cm,
so R = ½ (30 cm) = 15 cm →
m
15 cm x (1m/100cm)) = 0.15 m
a = 4 π2(.15m) / (3 s)2
a = 0.66 m/s2
Moon’s orbit
  The moon’s orbit (nearly circular) about the earth has a radius of
about 385,000 km and a period of 27.3 days. Determine the
acceleration of the moon toward the earth.
  Solution
where
a = .0027 m/s2
Summary
  An object is undergoing uniform circular motion
if it moves around a circle at a constant speed
  While the speed is constant, the object's
velocity is not constant. This is because the
direction of the velocity constantly changes as
the object moves around the circle
  Because the velocity is not constant, we know
the object must be accelerating
  The direction of acceleration toward the center
of the circle
  Centripetal acceleration
Centripetal Force
 If there is an acceleration toward the
center of the circle, there must be a
FORCE causing it.
 centripetal means “center seeking”
 Circular motion ALWAYS has a centripetal
force associated with it.
Centripetal Force
 Centripetal means “center seeking”
Centripetal Force
 Centripetal means “center seeking”
vs.
 Centrifugal means “center fleeing”
Force