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Circular Motion

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  1. Circular Motion

  2. Circular Motion • Definition: • Uniform Circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path

  3. 2.4.1Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the center of the circle. • Axis – the straight line around which rotation takes place • Rotation – a spin around an internal axis. i.e.: a carnival ride or record (big CD) • Revolution – a spin around an external axis. i.e.: the Earth around the sun

  4. 2.4.1Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the center of the circle. • Speeds for objects in a straight line are called linear (or tangential) speeds, • Linear speeds are a rate at which an object covers a certain distance (v =d/t) • Ex. Unit – m/s , km/hr , mph

  5. Can’t express speeds of rotation with a linear speed, • b/c objects at different points on the rotating object have different linear speeds • Rotational speed • Expresses the rate at which an object rotates through a portion of a circle ( an angle) • Ex. Unit --- RPM’s

  6. Are all people on Earth moving at the same speed?? • Earth is rotating about an axis through its poles • So that means we are all moving since we are all on the Earth.

  7. Below, a record spinning on a axis through its center (black dot) • Faster linear speed, Star or Smiley?? Smiley, travels a greater distance for each Full spin. • Faster rotational speed, Star or smiley?? • Both the same, b/c entire record is rotating at the same rate

  8. Are some of us moving with a greater LINEAR SPEED than others?? • Yes, closer to the Equator, the faster you are moving…. Closer to poles, the slower you are moving • Are some of us moving with a greater ROTATIONAL SPEED than others?? • No, all people on earth have same rotational speed, because Earth is spinning at the same rate everywhere

  9. Velocity was… v = d/t • Distance is now the circumference of the circle (2πr) • Period (T) is the time it takes for one revolution. • So… Speed = ? v = 2πr/T

  10. Velocity was… v = d/t • Distance is now the circumference of the circle (2πr) • Period (T) is the time it takes for one revolution. • So… Speed = ? • This is also called “Tangential Speed” v = 2πr/T

  11. Check Your Neighbor… • If a meter stick supported at the 0-cm mark swings like a pendulum from your fingers (look at demo), how fast at any given moment is the 100-cm mark compared to the 50-cm mark? It takes 2 seconds to make one complete rotation.

  12. 2.4.2Apply the expression for centripetal acceleration. • Think about a Ferris wheel. • The cars in on the Ferris wheel are in uniform circular motion. • Even though they have a constant vt, CAN the cars still have an acceleration?

  13. 2.4.2Apply the expression for centripetal acceleration. • This is due to what defines acceleration: a = vf – vi tf - ti • Because velocity is a vector, acceleration can be changed by the magnitude or direction of the velocity.

  14. 2.4.2 Apply the expression for centripetal acceleration. • Well, velocity has changed, so centripetal acceleration (ac) will be a little different too • Centripetal acceleration = (tangential speed)2 / radius of circular path • The acceleration is still a vector qty, and will always point toward the center of the circle. ac = v2/r

  15. 2.4.1Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the center of the circle. 2.4.2 Apply the expression for centripetal acceleration.

  16. Practice Problem 1 ac = vt2/r • A test car moves at a constant speed around a circular track. If the car is 48.2m from the track’s center and has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed? • What are you given? • Needed? • Vt = 19.7 m/s

  17. Answer:19.7m/s

  18. Practice Problem 2 ac = vt2/r • The cylindrical tub of a washing machine has a radius of 34 cm. During the spin cycle, the wall of the tub rotates with a tangential speed of 5.5 m/s. Calculate the centripetal acceleration of the clothes sitting against the tub. • What is given? needed? • A = 89 m/s2

  19. Answer = 89 m/s2

  20. Velocity Practice From Packet • Classwork: (Holt: Physics) pg236 Practice A

  21. Velocity Practice From Packet • 7 m/s • 0.26 m/s • 49 m/s

  22. Practice A Centripetal Acceleration • 2.5m/s • 11m/s • 1.5m/s2 • 58.4m

  23. Centripetal Acceleration • A bobsled travels at 34 m/s and goes around two turns in the track as seen here. What is the acceleration of the sled in each turn? Turn 1: 35 m/s2 Turn 2: 48 m/s2

  24. Centripetal Force • Any force that causes an object to follow a circular path • Watch the demo. (spinning cup of water) • What provided the Centripetal Force on the cup? • On the water? • Do you know how your washing machine works?

  25. 2.4.3 Identify the force producing circular motion in various situations. • Centripetal force is necessary for circular motion. • What would happen if the string attached to the cup broke?

  26. 2.4.3 Identify the force producing circular motion in various situations. ? • When driving in a circle, in what direction is a force acting on you? • Pushing you outward from the circle, or inward? • If you are swinging a yo-yo in a circle, and the string breaks…. What path does the yo – yo take?? • Ans. -- Inwards, toward the center of the circle • Ans -- yo- yo goes in a path tangent to the circle

  27. 2.4.3 Identify the force producing circular motion in various situations. • HOWEVER, People commonly think there is a force pushing you out from the circle • Feels like you are being pushed outward • Example ….. The Rotor- amusement park ride, a centrifuge, CD on your dashboard moving to the right when your turning left • Why is this??

  28. People Stand with backs against wall of a large cylinder, cylinder then starts spinning, and people are seemingly pushed against the wall, then floor drops, and people are stuck against the wall. http://www.youtube.com/watch?v=uz_DkRs92pM The Rotor

  29. So why is there no Force pushing you out from the circle?? • A force does not cause this…… your INERTIA does!! • Inertia makes you want to stay in a straight line, and by going in a circle, you are fighting your own inertia • This is how Rotor works, and why CD on dashboard happens • The only actual force acting on you is the Centripetal Force

  30. 2.4.3 Identify the force producing circular motion in various situations. • Centripetal means “center- Seeking” • Force pushes you toward the center of the circle • Is the force that keeps you moving in a circle, and keeps your inertia from taking you in a straight line Centripetal Force is affected by.. Mass (m), linear speed (vt), and radius (r)

  31. Centripetal Force • Inertia wants to take objects in a tangent line, to the circular path • Inertia is why you feel like your being pushed outward • This outward pushing is sometimes called the Centrifugal Force • but it is not actually a force, is only inertia • Every object that moves in circular motion must experience a centripetal force from somewhere

  32. Practice B pg 238

  33. Practice B pg 238 1) 29.6kg 2) 40m 3) 40N 4) 35m/s

  34. Can you identify the different sources of centripital force? Watch Video

  35. 2.4.3 Identify the force producing circular motion in various situations. • By definition – the net force that is directed toward the center of the circle. • This force is provided by a frame of reference • Consider a ladybug in a spinning can • The apparent centrifugal force on the lady bug is only an effect, not an interaction.

  36. Simulated Gravity • A spinning wheel can provide a “gravity” to occupants within it. • If multiple rings are built, the gravity would vary depending on distance from center. • Outer edge 1g, then ½ way is 0.5g

  37. Centripetal Force • The force equation will not change: • However, remember this is now Fc, so… F = ma Fc = mac or Fc = mv2/r

  38. Practice Problem 3 Fc = mv2/r • A bicyclist is riding at a angular speed of 13.2m/s around a circular track. The magnitude of the centripetal force is 377N, and the combined mass of the bicycle and rider is 86.5kg. What is the track’s radius? • What are you given? needed? • r = 40m

  39. Answer: 40m

  40. Vertical Circular Motion If an object is suspened on the end of a cord and is rotated in vertical circle what forces are acting on it? Lets watch Video #2 Lets draw an FBD.

  41. At the top We should see that the Fnet = Fc + Fg OR Ften = (mv2)/r + mg

  42. At the bottom We should see that the Fnet = Fc - Fg OR Ften = (mv2)/r - mg

  43. Practice Problem 4 • A 0.5kg mass, suspended on the end of a light cord, 1.2m long, is rotated in a vertical circle at a constant speed such that one revolution is completed in 0.4s. Calculate the tension in the cord when the weight is: • A) at the top of the circle • B) at the bottom of the circle

  44. Answer: A) 143N B) 153N

  45. Centripetal Acceleration • A bobsled travels at 34 m/s and goes around two turns in the track as seen here. What is the acceleration of the sled in each turn? Turn 1: 35 m/s2 Turn 2: 48 m/s2

  46. TOPIC 6.1: Gravitational Fields and Forces These notes were typed in association with Physics for use with the IB Diploma Programme by Michael Dickinson

  47. What is gravity? Is there gravity in space? Why do astronauts float? What keeps the moon from flying off in space?

  48. 6.1 Gravitational Force and Field 6.1.1 State Newton’s universal law of gravitation. Watch Veritesium Videos 1, 2, 3 http://www.youtube.com/watch?v=mezkHBPLZ4A&list=PL772556F1EFC4D01C http://www.youtube.com/watch?v=zN6kCa6xi9k&list=PL772556F1EFC4D01C http://www.youtube.com/watch?v=iQOHRKKNNLQ&list=PL772556F1EFC4D01C

  49. Two cars are parked 3m away from each other. One car has a mass of 1500kg while the other has a mass of 2000kg. What is the gravitational force between them?

  50. 6.1 Gravitational Force and Field 6.1.1 State Newton’s universal law of gravitation. • Galileo (1564-1642) – g = 9.81m/s2, even with different masses. • David Scott – feather and hammer dropped on the moon, Apollo 15 • Isaac Newton(1643-1727) – • Idea about a cannon ball that never hit the ground. • Orbit period of the moon – 27.3days • Radius of moons orbit – RM = 3.844 x 108m, RE = 6.378 x 106m • mid-1600s Earth’s and Moon’s masses had been determined • MM = 7.35 x 1022kg • ME = 5.98 x 1024kg)