Circular Motion

1. Circular Motion

2. Circular Motion • Which of the following are accelerating? • A car slowing down • A free-fall object momentarily stopped at its maximum height • A ball connected to a string, being swung in circles at a constant speed? • Justify your answer • ALL are accelerating because acceleration is a change in velocity = change in speed or a change in direction

3. Circular Motion Basics • Velocity is always tangent to path • Force and acceleration are always in the same direction, towards the center of the circle

4. Discussion Question 1 At the position shown, what is the direction of the centripetal force acting on the airplane? North South East West

5. Circular Motion • On the Gravitron ride you feel like you are being pushed outwardsby the centrifugal force • Centrifugal Force is an fictitious force • pulling you outwards • It does not exist!

6. Centripetal Force • In reality, what you feel is the force of the wall pushing you in due to inertia • CentripetalForce = any force that pulls you inward causing you move in a circle • Examples: • Normal force of a wall • Tension of a string

7. Checkpoint • Imagine: if you drove into a wallwhat would you feel? You’d feel a “push” forwards

8. Centripetal Force • What “threw” the driver over wall? • Inertia! (kept doing what they were doing)

9. Centripetal Force • Inertia is at work in a turn also

10. Centripetal Force • The “centrifugal” outward force you feel is your inertia • If you removed the gravitron wall you would fly out tangent to the circular path

11. Lets practice! • Questions #1- 2 pg 374

12. Centripetal acceleration • Acceleration due to the change in direction of velocity (rather than the speed of the object) • ac always points towards the circle’s center Constant speed Distance to the point of rotation

13. Centripetal acceleration • Imagine twirling a ball on a string • What affects its acceleration? • Speed of the twirl • Length of the string

14. Calculating Centripetal Force Centripetal acceleration Distance to the point of rotation • Now let’s mix it with Newton’s Second Law

15. Circular Velocity • Average speed can be found with • The time it takes to complete 1 rotation is called the period (T) • (units: s) • In a circle, the distance traveled in oneperiod is the circumference, 2πr

16. Centripetal Force • Plugging the new v into centripetal force gives:

17. Example: Imagine twirling a 0.50 kg ball on a 0.80 m long string. The ball moves in a circle at a rate of 1.25 rotations per second. How much force is required to keep the ball moving this way? given: want:

18. Centripetal Force • Plug them in

19. Time for lab Turn to pg. 443

20. Labbete • Make sure you attach more than 3 washers to your string • Do not let the tape on your string hit the tube or move significantly white you are counting the # periods • Count the periods carefully • Period is measured in seconds!

21. Labbete Hints • Period is measured in seconds! Look at the units and the example problem in your Cornell notes • Do not confuse the mass of your stopper with the mass of your washer.

22. Example 1 A tennis ball tied to a string rotates CCW at constant speed as seen from above. At the points iand iii, which arrows best describe the centripetal force (net force) vectors for the ball? point ipoint iii ii iii i A. B. C. D. Net force is zero due to constant speed. iv Top View

23. Example 2 A tennis ball tied to a string rotates CCW at constant speed as seen from above. At the points i and iii, which arrows best describe the instantaneous velocities of the ball? point ipoint iii ii iii i A. B. C. D. Velocity vectors are not straight at points A and C. iv Top View

24. Net Force = Centripetal Force • Any time an object accelerates centripetally, there must be a net force towards the circles center causing the acceleration • For circular motion:

25. Net Force = Centripetal Force • The force acting as could be…. • … tension (ex: a ball on a string) • … friction (ex: a car turning) • … gravity (ex: orbit)

26. Horizontal Circular Motion • The centripetal force is not a new force, it’s just the net force that makes an object move in a circle • When moving in a horizontal circle, friction orWxbecomes important.

28. A 2000 kg car rounds a circular turn of radius 30m. If the road is flat and the coefficient of static friction between the tires and the road in 0.67 what is the fastest velocity the car can have as it rounds the corner without skidding?

29. Vertical Circular Motion • Sometimes, more than one force contributes to the • When moving in a vertical circle, gravity becomes important. • Net force at each part of ride varies.

30. Bottom of the ride • At the bottom, the FN pushes the seat up. • This pulls the seat againstyour weight. • Feels heavier FN mg

31. Normal Force at the bottom • At the bottom of the ride: NB • Notice FB gets stronger the faster the ride goes. mg

32. Normal Force at the top • At the top of the ride the acceleration points down (negative): FT mg • Opposite situation at the top

34. 18 A 40kg child takes a ride on a roller coaster. A certain portion of the ride involves vertical loops (that can be approximated as circular), each with a diameter of 18m. If the coaster passes through the loops at a rate of 25m/s, what force does the seat exert on the child at the lowest point of one of the loops?

35. Gravity • Not everything thrown up must come down! • The higher something goes the smaller the effect of earth’s gravity on it. • If you throw it hard enough, “g” becomes too small to slowit to a stop. • This is called the escape velocity • escape velocity from earth = 25,000 mph

36. Gravity • Gravity is not only caused by large planets, moons and stars. • Everything with mass attracts everything else with mass no matter the distance • Unless the mass is really large, you will not notice it

37. Anthrocentric Universe • Aristotle reasoned that all objects wanted to be at the center of the universe… • The Earth! • all objects circle Earth

38. Heliocentric Universe • Copernicus noticed that the planets did not stay the same distance from the earth. • He used observations to come up with a new theory. • All objects circle the sun

39. Tycho and Kepler • Tycho Brahae spent 20 years trying to proves Copernicus wrong with very careful measurements of the planets. • Compromise • Planets circle both the Earth and sun.

40. Universal Law of Gravity • Isaac Newton noticed that the force making the moon go around the earth was the same as the force causing an apple to fall. • “Between any two masses there exists an attractive force of gravity that is proportional to the product of the masses and inversely proportional to the square of the distance between their centers.”

41. Universal Law of Gravity • This gives the expression: • or, the equation: • G = universal gravitational constant

42. Proportionality exampleQuestion #1 pg386

43. Gravitational Constant • Newton never was able to calculate “G” • Because, if you rearrange to calculate: • You find that measuring each of the variables is easy until you get to force. • The force between materials on earth was too small for Newton to detect.

44. Measuring “G” • Henry Cavendish used an apparatus made by John Michell.

45. Measuring “G” • Used hanging lead balls. • Force of gravity can be found by measuring the tiny angle the small balls moved

46. Mass of the Earth • Cavendish’s main reason to calculate G was to use it to find the mass of the Earth. • Imagine any object on the Earth’s surface. It’s force due to gravity Fg = mg. • Since height of any object on Earth is negligible, R is just Earth’s radius.

47. Mass of the Earth • The radius of the Earth had been calculated way back in 200 BC

48. Time to practice Turn to pg. 386

49. Satellite Motion • Imagine standing on a really tall building and throwing a ball really hard. • The ball would follow a parabolic path and land in front of the building.

50. Satellite Motion • Now throw it harder. • Same thing except balls goes a little farther.