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.

Centripetal Acceleration Acceleration directed toward a central point Changes direction of velocity but not magnitude Causes circular motion

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 F T – mg = mv 2 /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 F T + mg = mv 2 /r If ball is moving too slowly, centripetal force < weight, ball will fall out of circular path

v v FTFT FTFT 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. mv 2 /r = mg, so:

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