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Circular Motion

Circular Motion. Circular Motion Centripetal Acceleration Centripetal Force Center of Mass Torque Rotational Inertia & Angular Momentum. Circular Motion. True circular motion is motion that follows a path around a center point.

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Circular Motion

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  1. Circular Motion • Circular Motion • Centripetal Acceleration • Centripetal Force • Center of Mass • Torque • Rotational Inertia & Angular Momentum

  2. Circular Motion • True circular motion is motion that follows a path around a center point. The path maintains a constant distance from the center point (the radius). We call the time it takes to go around once the Period (T) r 0 T

  3. Revolution – the center point is outside the object (like the earth revolves around the sun) Rotation – the center point is inside the object (like the earth rotates around its axis.) Circular Motion • The two main types of CM are rotation and revolution.

  4. How fast does a rotating object travel? • How far does it go in one rotation? • 2πr (the circumference) • How long does it take to make one rotation? • T (the period) • So speed = distance/time =2πr / T • Sometimes called linear speed 1 rotation

  5. Velocity or Tangential Speed v • At any instant, the object’s velocity is tangent to the circle • The velocity vector shows the direction the object is going at that instant • Magnitude of v is constant • Direction is always changing v

  6. Rotational Speed • Sometimes we specify how fast an object rotates with a rotational speed • Number of rotations per second • = # rotations # secs • Sometimes called the frequency • f = 1/T 5 rot/s

  7. What’s the Difference? Two bugs spin on a record: • Which bug has a greaterrotational speed? • They are equal! (they both go around the same number of times per second) • Which bug has a greaterlinear speed? • The red bug. Bigger radius, bigger total path for each rotation.

  8. Center of Gravity and Rotation • Circular Motion • Centripetal Force • Centripetal Acceleration

  9. Newton’s 1st Law v • … basically velocity will not change without a net force applied • In circular motion, • Magnitude of v is constant • Direction is always changing • So velocity is changing, and there must be a net force v

  10. v Fc r Centripetal Force The direction is always straight toward the center of the circle

  11. Question I whirl a bucket of water in a big vertical circle. The water stays in the bucket. What keeps the water in the bucket?

  12. Question What keeps the water in the bucket? The centripetal force keeps the bucket moving in a circle, which keeps the water from flying outward The water’s inertia makes it want to continue in the same speed & direction

  13. Removing the Force • The velocity vector shows the direction the object is going at that instant • Remove Fc, and the object will continue in the same (tangential) direction v

  14. A ball in a car • A ball (red circle) is in a car (blue circle) • If the car turns to the left (a centripetal force due to frictional force on the tires), • but the ball is free to roll (low friction- no centripetal force), • The ball will continue in the same direction it was moving (due to inertia)

  15. Center of Gravity and Rotation • Circular Motion • Centripetal Force • Centripetal Acceleration

  16. Centripetal Force • From Newton’s Second Law, we know that a = Fnet/a, or Fnet = ma. • A non-zero net force on an object will make the object accelerate. • Fc is our net force, so Fc = m ac where ac is the centripetal acceleration

  17. Centripetal Acceleration Wait a minute: the speed is constant! How is it accelerating? • Acceleration is a change in velocity • Velocity has a magnitude and direction • In circular motion, we’re using constant magnitude (speed), but the direction is always changing • Therefore, there’s an acceleration

  18. Centripetal Acceleration ac = v2/r “v” is the linear velocity of the object. “r” is the radius of the circular motion.

  19. v ac r Centripetal Acceleration The direction is always straight toward the center of the circle (it has to be the same direction as the force)

  20. “Pulling 3 g’s” • g is the acceleration due to gravity (9.81 m/s2 at the surface of Earth) • Sometimes high accelerations are stated in multiples of g • Example: 3 g’s would be 3 x g, or about 30 m/s2 • If you can make something in outer space accelerate at 1g, it will feel like it’s experiencing Earth’s gravitational pull

  21. Why Not “Centrifugal” (Center-Fleeing)? • Centripetal force is the force on the rotating object, keeping it on a circular path • There is not a “centrifugal force” on the object • But there is a centrifugal force on whatever is pulling it, due to Newton’s 3rd Law • In the bucket example, the arm puts a centripetal force on the bucket • The bucket puts an equal and opposite (centrifugal) force on the arm

  22. Circular Motion Lab What factors do you think could affect the amount of centripetal force that an object feels while in circular motion?

  23. Circular Motion Lab Purpose Question: What is the effect of changing _________ on centripetal force? Choose: Radius Mass Rotational Speed

  24. Hypothesis What types of relationships are possible between the variables that we are testing in the Circular Motion Lab? (What have we seen so far this year?) Sketch a prediction graph for each of the variables (even if you’re not testing it): FC FC FC RPM’s Radius Mass

  25. Circular Motion Lab Observations and Results: Display your data in a table and in a graph. Note observations that were made while testing. Conclusion: Emphasize the relationship that you discovered between your variable and the centripetal force. Use data to support your conclusion. Include possible errors.

  26. Circular Motion Problems Example: A merry-go-round is 6 meters in radius and takes 10 seconds to go around in a circle. • What is the rotational speed of the merry-go-round (in rotations per second)? f = # of rotations/# secs = 1 rotation/10 seconds = .1 rotations per second

  27. Circular Motion Problems Example: A merry-go-round is 6 meters in radius and takes 30 seconds to go around in a circle. • What is the linear speed at the outer edge of the merry-go-round ? v = d/t Find distance around circle (circumference): C = 2πr = 2(3.14)(6) = 37.7 m Divide distance by time to get linear speed: v = d/t = (37.7 m)/(10 sec) = 3.77 m/s

  28. Circular Motion Problems Example: A merry-go-round is 6 meters in radius and takes 30 seconds to go around in a circle. • What is the centripetal acceleration of the merry-go-round ? ac = v2/r = (3.772)/6 = 1.7/6 = 2.37 m/s2

  29. Circular Motion Problems Example: A merry-go-round is 6 meters in radius and takes 30 seconds to go around in a circle. D. What is the centripetal force on a 100-kg person riding on a horse near the outside? fc = m * ac = 100kg * 2.37 m/s2 = 237N

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