Round and Round 2-2-3 Circular Motion

Uniform Circular Motion Objects traveling in circular motion have constant speed and constantly CHANGING velocity – changing in direction but not magnitude How do we define VELOCITY? Velocity is TANGENT to the circle at all points What ‘d’ are we talking about? What ‘t’ are we talking about? PERIOD (T) Time for one revolution CIRCUMFERENCE C = 2πr = πd If this is true, why does ANYTHING move in a circle?

Centripetal Force Inertia causes objects to travel STRAIGHT Paths can be bent by FORCES CENTRIPETAL FORCE bends an object’s path into a circle - pulling toward the CENTER

Misconception The doors to the “Gravitron” close and it starts to spin. You are pushed against the outside edge of the ride and pinned there, You must be experiencing “centrifugal force” throwing you outward from the ride! Right?

What is really happening? F As the Gravitron starts to spin, friction between your body and the ride start you moving v Once you are moving, your body wants to go STRAIGHT … but you can’t… The wall keeps pushing you back in toward the center of the ride!

What is the sensation that you feel? centrifugal (center fleeing) force A ‘fictitious’ or ‘inertial’ force that is experienced from INSIDE a circular motion system – WHAT YOU FEEL centripetal (center seeking) force A true force that pushes or pulls an object toward the center of a circular path – WHAT ACTUALLY HAPPENS

Centripetal Acceleration Centripetal force is a NET FORCE Causes ACCELERATION In the SAME DIRECTION AS NET FORCE

Example #1 What is the centripetal acceleration of a toy ball on the end of a 1.44 meter long string if it is moving at 12 meters per second? ac = v2/r ac = (12 m/s)2/1.44 m ac = 100 m/s2

Centripetal Force

Example #2 What is the centripetal force acting on a 2000 kilogram airplane if it turns with a radius of 1000 meters while moving at 300 meters per second? ac = v2/r ac = (300 m/s)2/1000 m ac = 90 m/s2 Fc = mac Fc = (2000 kg)(90 m/s2) Fc = 1.8 x 105 N

Example #3 Is it possible for a 1000 kilogram car to make a turn with a radius of 50 meters while moving at 15 meters per second with rubber tires on dry asphalt? Fc = 4500 N Ff = 8339 N Fc = mv2/r Fc = (1000 kg)(15 m/s)2/ 50 m Fc = 4500 N Ff = μFN Ff = (0.85)(9810 N) Ff = 8339 N Yes, as long as Ff ≥ Fc

End of 2.2.3 - PRACTICE