Transcript Motion in a Circle

Uniform Circular
Motion
Motion in a Circle
Revolution: If entire object is moving in
a circle around an external point. The
earth revolves around the sun once a
year
 Rotation: Axis of rotation is internal and
passes through object. The earth
rotates on its axis once a day

Circular Motion
Acceleration is always present since
direction is always changing.
 Force must be applied to cause
acceleration.
 Can be uniform (constant speed) or
variable with tangential acceleration

Centripetal Force
Force directed towards the center of a
circle
 Causes centripetal acceleration.
 Can be supplied by tension in a string,
friction, gravity, pushing from another
object, etc.
2

v
2
Fc  m  m r
r
Centripetal Acceleration
Acceleration directed toward a central
point
 Changes direction of velocity but not
magnitude
 Causes circular motion

2
v
2
ac    r
r
Motion in a Vertical Circle
Effect of gravity must be considered
 Consider ball on string, moving in circle
at a constant speed
 At bottom of circle, tension in string
must provide the centripetal force to
change the direction of the ball and
support the weight of ball
 FT – mg = mv2/r

Motion in a Vertical Circle

At top of circle, the weight is directed
towards the center of the circle providing
part of the centripetal force
 Tension in string and the weight combine to
provide the centripetal force
 FT + mg = mv2/r
 If ball is moving too slowly, centripetal force
< weight, ball will fall out of circular path
FT
Fg
FT
v
Fg
v
Critical Velocity
Minimum velocity needed for object to
follow circular path.
 At this velocity, the weight provides all
the centripetal force at top of circle:
string tension is zero
 Depends only on radius of circle and
gravity, not on the mass of the object.
 mv2/r = mg, so:
vc  rg

Centrifugal Force
Not an actual force.
 Only exists for observer in accelerating
reference frame.
 Makes objects appear to move away
from axis of rotation.
 Actually due to inertia of objects which
makes them tend to continue straight
line motion

Frame of Reference





System for describing location of objects
In inertial reference frames, law of inertia
holds true.
Non-inertial frames are accelerating and
appear to violate law of inertia.
Relativity is study of relationships between
events in different reference frames
Centrifugal force can be used to describe a
non-inertial frame of reference