“What is uniform circular motion?”

3. “What is uniform circular motion?”

4. In uniform Circular motion a body travels at a constant speed on a circular path.

5. The speed is constant, ‘v’ The velocity is not! There is an acceleration There is a net force Link

6. T = Period (time per revolution) f = frequency (revolutions per unit time) v = speed r = radius

7. To the center To the center

9. Constant Speed not Velocity: The direction of v changes continually! The velocity is always tangent to the path

10. There must be a force and therefore an acceleration: Directed to the center

11. When the string is cut it flies off on a ______. Tangent

12. since then

13. Mike flies his model plane, the radius of the orbit is 50 m • and the 2 kg plane is flying at 20 m/s. • What is the tension he feels in his hand? • What was the centripetal acceleration of the plane? • At the position shown draw in vectors showing the direction • of the force, acceleration, and velocity.

14. A 95-kg halfback makes a turn on the football field. The halfback sweeps out a path which is a portion of a circle with a radius of 12 m. The halfback makes a quarter of a turn around the circle in 2 s. Determine the speed, acceleration and net force acting upon the halfback. Speed along the path

15. A 900-kg car moving at 10 m/s takes a turn around a circle with a radius of 25.0 m. Determine the acceleration and the net force acting upon the car. • a = (v2)/R • a = (10.0 m/s)2/(25.0 m) • a = (100 m2/s2)/(25.0 m) • a = 4 m/s2 • 2. F = ma = (900 kg) x (4 m/s2) • F = 3600 N

16. STOP HERE (12/8/15)

17. Not enough friction to turn the tape!

18. Jeff Gordon leads his race and must drive into a curve at top • speed to win it all. The radius of the curve is 1000 m and the • coefficient of static friction between his tires and the dry • pavement is 0.50. • Find the maximum speed he can have and still make the turn. • Which force “provides” the centripetal force?

20. Centripetal Force depends on the mass: Smaller mass  Smaller force

21. Centripetal Force depends on the velocity Smaller velocity  Smaller force

22. Centripetal Force depends on the radius Smaller radius  Larger force

23. In this animation, the "sticky" or adhesive forces from the tire tread act as the centripetal force. It’s large enough to keep the mud in a circular path as the tire spins. The tire is spinning faster here which means a larger centripetal force is needed to keep the mud in the circular path. The adhesive force is not large enough, it flies off on a tangent and follows Newton's first law!

24. Hell Hole • The rotor is an amusement park ride where people stand against • the inside of a cylinder. Once the cylinder is spinning fast • enough, the floor drops out. What force keeps the people from • falling out the bottom of the cylinder? • Centripetal force • Friction • Normal force  correct

25. At amusement parks there is a popular ride where the floor of a • rotating cylinder room falls away, leaving the backs of the riders • “plastered” against the wall. Suppose the radius of the room is • 3.3 m and the speed of the wall is 10m/s when the floor falls away. • How much centripetal force acts on a 55 kg rider? • What is the minimum coefficient of static friction that must exist between • the rider’s back and wall, if the rider is to remain in place when the wall • falls away?

26. Newton’s Second LawApplied to Circular Motion • String provides the tension (FC ) • This force is directed toward the center

27. Vertical Circle

28. Conical Pendulum

29. No acceleration in the vertical direction The centripetal force is provided by Conical Pendulum A component of the tension provides the centripetal Force

30. TOP BOTTOM Ferris Wheel

31. Ferris Wheel Find an expression for the maximum speed at which the ferris wheel can rotate before turning its passengers into projectiles. Making the passengers airborne is the same as saying FN = 0, therefore: Note: It’s independent of the mass of the riders

32. The normal forces between the roller coaster and tracks • The normal forces between you and the roller coaster

34. Sign Convention: • To the center is positive • Away from the center is negative

35. Fc = w - n = mv2/r mg - n = m v2 / r n = mg - m v2 / r Calculate the normal force in each case if the mass of the kids plus car is 2,000 kg, v = 3 m/s, and r = 5 meters Fc = n – mg = m v2 / r n = mg + m v2 / r

36. Geosynchronous Satellites To serve as stationary relay station the satellite must be placed at a certain height above the earth surface • they have an orbital period equal to the rotational period of the earth, 24 hours.

37. Military Communications

38. SUMMARY Particle moving with uniform speed v in a circular path with radius r has an acceleration aC : • The acceleration points to • the center of the circle! • Centripetal acceleration

39. The velocity of the particle is always __________ • The centripetal acceleration is towards the __________ • The centripetal force acting on the particle is towards the ______ • Centripetal force causes a • change in the ______________ • but no change in ___________ • The magnitude of the centripetal • acceleration is: a = _________ • Newton’s law: The force on the • particle is (centripetal force) • F = m·a = ______________

40. Motion in a circular path at constant speed • Velocity is changing, thus there is an acceleration!! • Acceleration is perpendicular to velocity • Centripetal acceleration is towards the center of the circle • Magnitude of acceleration is • The change in velocity is director to the center

41. Horizontal Circle • Lauren rotates a stone, m = .50 kg that is attached to the end of • a 1.5 m cord above her head in a horizontal circle. • If the cord can hold 50 N of tension, at what maximum speed • will it rupture. • Which force “provides” the centripetal force?

42. A particle is moving in a circular path. If the force on the particle would suddenly vanish (string cut) in which direction would the ball fly off?

45. FN cos FN W a Banked Curve FN sin

50. Le circular motion !