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.

rmr

vmFc

22

Centripetal Acceleration

Acceleration directed toward a central point

Changes direction of velocity but not magnitude

Causes circular motion

rr

vac

22

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

v

v

FT

FTFg

Fg

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:rgvc

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