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Aim: How can we describe circular motion?

Aim: How can we describe circular motion?. Circular Motion. How can we describe circular speed?. Objects traveling in circular motion have SPEED. How do we define SPEED ?. Velocity is TANGENT to the circle at ALL POINTS. What ‘d’ are we talking about?. What ‘t’ are we talking about?.

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Aim: How can we describe circular motion?

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  1. Aim: How can we describe circular motion? Circular Motion

  2. How can we describe circular speed? Objects traveling in circular motion have SPEED How do we define SPEED? 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?

  3. How can we define 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

  4. 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?

  5. Can you explain what is really happening? As the Gravitron starts to spin, friction between your body and the ride start you moving vc Fc Once you are moving, your body wants to go STRAIGHT … but you can’t… The WALLS push you back in toward the center of the ride!

  6. What is it you feel? • centrifugal (center fleeing) force • A ‘fictitious’ or ‘inertial’ force that is experienced from INSIDE a circular motion system • centripetal (center seeking) force • A true force that pushes or pulls an object toward the center of a circular path

  7. How can we calculate Centripetal Acceleration? Centripetal force provides an unbalanced, net force toward the center of a circular path Unbalanced forces cause ACCELERATION v , Fc , andac constantly CHANGE DIRECTION, but not MAGNITUDE

  8. Example #1 Determine the centripetal acceleration of a toy ball swinging with a speed of 12 meters per second on the end of a 1.44 meter long string. ac = v2 / r ac = (12 m)2 / (1.44 m) ac = 100 m/s2

  9. Example #2 Determine the velocity of a car that experiences a centripetal acceleration of 6 meters per second2 as it moves through a turn with a radius of 5 meters. ac = v2 / r 6 m/s2 = v2 / (5 m) v = 5.48 m/s

  10. Calculating Fc Newton’s 2nd Law? F = ma

  11. Example #3 What is the centripetal force on a 2000 kilogram airplane making a turn with a radius of 1000 meters if it is moving at 300 meters per second? Fc = mv2 / r Fc = (2000 kg) (300 m/s)2 / (1000 m) Fc = 180,000 N

  12. Example #4 How far from the center of a merry-go-round is a 500 kilogram horse that is traveling at 3 meters per second if it experiences a force of 3000 newtons? Fc = mv2 / r 3000 N = (500 kg) (3 m/s)2 / r r = 1.5 m

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