circular motion

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circular motion
2015-01-12 05:08:50
physics unit

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  1. if a particle , moving along a circle passes an equal arc length in equal time , this is called
    uniform circular motion
  2. linear velocity
    • arc length per unit time
    • instantaneous velocity of a body in circular motion
  3. v =
    • s/t 
    • where v = linear velocity 
    • s = arc length 
    • t = time taken
  4. linear velocity is a ... quantity
  5. the direction of one point in circular motion is
    the tangent direction of the circumference at that point
  6. angular velocity/speed
    in rotation the angle turned through per second , units radians per second , rad s-1
  7. ∅ =
    • arc length/radius 
    • ∅=s/r
  8. one radian is defined as
    the angle subtended at the center of a circle by an arc equal length to the radius
  9. if we let the arc length become the entire circumference then s =
  10. the angle in radians generated in going around a complete circle is
  11. the angular change in full rotation is
    either 360 degrees or 2pi radians
  12. 2pi rad =
    360 degrees
  13. 1 rad =
  14. 1 degree =
    2pi rad/360
  15. angular velocity symbol =
  16. w =
    • v/r 
    • θ/t
  17. time period =
    the time a body in circular motion takes to complete one revolution , symbol T , units seconds s
  18. frequency
    • the number of revolutions per second , symbol f , units hertz , Hz , 
    • the reciprocal of time period 
    • T = 1/f
  19. rotational speed =
    angular speed/velocity
  20. if a body is in uniform circular motion along a circumference of radius r the arc it covers in a period T is
  21. hence the linear velocity , v , =
  22. hence w =
  23. T =
  24. hence w =
  25. the centripetal force is the
    resultant force required to keep an object of mass , m , moving at speed , v , on a circular path of radius r
  26. the magnitude of the centripetal force =
  27. the magnitude of the centripetal force is .... throughout motion
  28. the centripetal force always points
    towards the center of the circle and continually changes direction as the object moves
  29. from v = wr 
    F =
    • m(wr)2/r
    • F = mrw2
  30. from w = 2pi/T
    F =
    • mr(2pi/T)2
    • F = 4pi2mr/T2
  31. by newtons second law F = ma
    • mv2/r = ma 
    • v2/r = a

    • mrw2 = ma 
    • rw2 = a 

    • 4pi2mr/T2 = ma 
    • 4pi2r/T= a
  32. the centripetal acceleration vector always points
    towards the center and continually changes direction as the object moves
  33. s , displacement =
    a vector describing the difference in position of two points
  34. sometimes the displacement may be
    2r (see diagram in notes to know when this applies)
  35. a mass on the end of a string is whirled round in a horizontal circle at increasing speed until the string breaks . the subsequent path taken by the mass is a
    parabola in a vertical plane
  36. for a particle moving with uniform speed the kinetic energy of the particle is
  37. w =
    2pi x rpm/60
  38. if a wheel exceeds maximum rate of rotation the direction of motion of the particle immediately after it leaves the wheel will be at a
  39. mass is always in
  40. Figure 4 shows an aircraft which is flying in a horizontal circular path at constant speed (see notes , remember diagram ?) the aircraft has constant speed but not constant velocity explain why
    • velocity is a vector quantity  - direction of motion is continually changing
    • speed is a scalar quantity - magnitude of motion is constant
  41. the aircraft is banked
    the horizontal component of the support force is acting as the centripetal force
  42. what produces the force necessary to accelerate pilot
    reaction with seat/friction between passenger and seat
  43. forces when a mass is whirled in a circle in a vertical plane 
    tension at different points
    • (see notes remember diagram ? )
    • tension at the top is lowest
    • tension at the bottom is highest 
    • top F = tension + mg 
    • bottom F = tension - mg
  44. 1 Figure 1 shows a space station that simulates gravity (artificial gravity). The station is designed in the shape of a cylinder which rotates about its long axis. (remember diagram) 
    artificial gravity appears to act ..... 
    centripetal force acts ........
    astronaut experiences .......
    • outwards from the center towards the wall 
    • inwards on astronaut 
    • a reaction force of feet
  45. angular displacement =
    • angle turned through in a given time 
    • 2pit/T 
    • 2pift
  46. angular speed/velocity =
    angular displacement per second
  47. centripetal force for a car going round a roundabout
  48. centripetal force for ball on a string
    tension in string
  49. centripetal force for earth moving round sun
  50. see diagram in notes hard to explain
  51. banking reduces centripetal force because
    the horizontal component is reduced
  52. 15m from axis of rotation means
    15m is the radius
  53. for a particle moving in a circle with uniform speed there's sometimes displacement of the particle in the
    direction of the force
  54. for a particle moving in a circle with uniform speed the force on the particle has constant magnitude and is always
    perpendicular to the velocity of the particle
  55. for a particle moving in a circle with uniform speed the kinetic energy of the particle is