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Circular Motion

Learn about circular motion, centripetal force, and their relationship. Discover how to calculate centripetal acceleration and observe circular motion examples.

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Circular Motion

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  1. CircularMotion Kathy Buckland

  2. What is Circular Motion? • The circular path along which an object travels • The rotation around a fixed axis What is the word used to describe this path? ORBIT

  3. Examples • Rollercoaster • Swinging an object on a string • Planetary objects-moon, satellites, etc. • Car going around a round-about

  4. Back to the mid 1600’s… Newton’s Second Law: “Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur” -Principia Mathematica (1687) Otherwise known as… F=force (N) m=mass (kg) a=acceleration (m/s2)

  5. F=maWhat is FORCE? • PUSH or a… • PULL

  6. Gravity Impact Forces Tension Friction Examples of Forces

  7. Circular Motion and Force How does the object stay in its path? This force is called… CENTRIPETAL FORCE centrum "center" and petere “go to” or “seek” To get where you want “to go”, you must…. PEDAL….

  8. Tension Friction Planetary Motion Car going in circles Not a new force !! Examples of forces: • Gravity • Impact Forces Examples of these “acting” as the CENTRIPETAL FORCE • Ball on a string • Rollercoaster

  9. What next? MASS • The amount of MATTERan object contains • Not weight -weight changes depending on gravitation field

  10. and finally… ACCELERATION How the velocity changes in a certain amount of time In physics lingo • a=acceleration (m/s2) • Δ= “change in” • v=velocity (m/s) • t=time (s)

  11. 2007 Lamborghini Murcielago LP640 acceleration: 0-62 mph time of 3.4 seconds (0-100km/h in 3.4 seconds!)

  12. ACCELERATION How the velocity changes in a certain amount of time In physics lingo • a=acceleration (m/s2) • Δ= “change in” • v=velocity (m/s) • t=time (s)

  13. Velocity vs. Speed • Velocity has a DIRECTION and a MAGNITUDE • The speed is the MAGNITUDE How do we represent direction and magnitude? VECTORS

  14. Vector Recall The length of the vector represents the MAGNITUDE or SPEED The direction it points is the DIRECTION Adding: Subtracting: (remember) a a+b a a-b b b

  15. Back to Circular Motion… How can we find the force it takes to hold on object in orbit? Remember: Δv is a change in directionnot magnitude

  16. DEMO # 1 Finding centripetal acceleration

  17. What will it be?

  18. How do we get centripetal acceleration ? Three more steps.. 1. Make a tiny triangle so.. • have a right triangle • use sinθ = opposite hypotenuse • sin θ = θ 2. Use similar triangles 3. Use some algebra Find similar triangles t2 A little geometry and algebra… t1 S=v(t2-t1)=vΔt

  19. Centripetal acceleration is…

  20. Finally put it all together… For circular motion…

  21. DEMO # 2 Observing the relationship

  22. The difference in force holding the object in circular motion can be seen as the device spins. As the velocity increases the changes in force become greater.

  23. Force comparisons… Compare to lifting up objects- Remember acceleration is gravity≈10 m/s2 1 N≈ force required to hold up an orange 10 N≈ force required to hold this weight Force to lift an elephant? m ≈ 4500 kg so… F ≈ 45000 N !! like lifting 40000 oranges

  24. And us ? Mass Earth ≈ 6 x 1024 kg v ≈ 30 000m/sec r ≈1.5 x 1011 m F ≈ 3.6 x 1022N Like lifting about 8 x 1017 or 800 million billion elephants !!

  25. What to remember • What circular motion is- be able to recognize it • Newton’s Second Law- you will see it again! • That velocity has direction and speed • Centripetal acceleration deals with the change in direction • Things that effect centripetal force are mass, velocity, and the distance from the center

  26. DEMO # 3 Observing Circular Motion

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