A level physics circular motion

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A level physics circular motion
2014-09-18 12:58:45
circular motion

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  1. define angular speed
    • the angle turned through per second when an object is in rotation 
    • unit radians per second
  2. centripetal acceleration
    an acceleration towards the center of a circular path
  3. centripetal force
    • a force causing an object to move in a circular path ; it acts towards the center 
    • units Newtons
  4. frequency
    • the number of oscillations or waves per second 
    • units hertz
  5. period
    the time taken for one complete oscillation or one full rotation
  6. uniform circular motion
    when an object rotates at a steady (constant) rate
  7. angular displacement
    • the angle turned through in a given time when an object is in rotation 
    • units radians
  8. circumference of the wheel
    • 2 pi r 
    • units meters
  9. frequency of rotation
    f = 1/T where T is the time for one rotation
  10. speed at any point on the perimeter
    • 2 pi r / T 
    • r is in meters
    • T is in seconds 
    • and the speed is in m/s
  11. angular displacement (radians) =
    • 2 pi t / T 
    • where t = duration and T = time for one rotation

    2 pi f
  12. in time , t , an object in uniform circular motion at speed v moves along the arc of the circle through a distance (in meters)  :
    • s = vt
    • where s = distance , v=speed and t=time 
    • s = 2 pi r t / T 
    • s = θr 
    • s = wrt
  13. angular speed (rad/s)  =
    2 pi rpm/60
  14. rpm means
    revolution per minute
  15. to convert from degrees to radians
  16. to convert from radians to degrees
    x 180/pi
  17. the velocity of an object in uniform circular motion isn't constant because
    the direction is continually changing , because velocity changes the object must accelerate
  18. the velocity of an object in uniform circular motion at any point is
    along the tangent to the curve at that point
  19. to make an object move round on a circular path , it must
    be acted on by a resultant force which changes its direction of motion
  20. the resultant force on an object moving round a circle at constant speed is called
    centripetal force because it acts in the same direction as the centripetal acceleration which is towards the center of the circle
  21. for an object whirling round on the end of a spring , the .... is the centripetal force
    tension in the string
  22. for a satellite moving round the earth .... is the centripetal force
  23. for a capsule on the london eye , the centripetal force is the
    resultant force of the support force on the capsule and the force of gravity on it
  24. any object that moves in circular motion is acted on by
    a resultant force which always acts towards the center of the circle . the resultant force is the centripetal force and therefor causes centripetal acceleration
  25. for a car travelling on the top op a hill
    the support force from the road on the vehicle is directly upwards in the opposite direction to weight
  26. the resultant force is
  27. the resultant force is the centripetal force so
    mg-s = mv2/r
  28. if the speed is greater than or equal to V0 then
    • the support force will = 0 and the car will loose contact with the road 
    • mg =mV0/r
  29. for a car on a roundabout centripetal force is
    the force of friction between the vehicles tyres and the road surface
  30. so the force of friction is
  31. for no skidding to occur the force of friction must
    • be less than a limiting value F0 and the speed of the vehicle must be less than a certain value V0
    • F0 =  mV02/r 
  32. some roads are banked to
    enable vehicles to drive round without any sideways friction on the tyres - this enables the speed to be greater .
  33. for there to be no sideways friction on the tyres due to the road
    the horizontal component of the support forces N1 and N2 must act as the centripetal force
  34. resolving these forces gives
    • (N1+N2)sinθ - horizontal 
    • (N1+N2) cosθ -0 vertical
  35. mv2/r =
  36. mg =
    (N1+ N2) cos θ
  37. tanθ =
  38. if v2 = gr then
    theres no sideways friction
  39. tension at the top is lowest because
    • at the top the weight and tension provide the centripetal force mv2/r = mg + R 
    • at the bottom the weight opposes tension mv2/r = S-mg 
    • the magnitude of mv2/r is constant round the circle
  40. on a swing the maximum speed is when
    • the spring passes through the lowest position 0.5mv2 = mgΔh 
    • v2=2gΔh
  41. at the lowest point S-mg =
    mv2/r = m2gh/r