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Moving in circles

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How can we recognise uniform motion in a circle?...

How can we recognise uniform motion in a circle?
What do we need to measure to find the speed of an object moving in uniform circular motion?
What is meant by angular displacement and angular speed?

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Moving in circles Moving in circles Presentation Transcript

  • Moving in Circles What forces are on you when you go around a corner?
  • Task
    • Try and explain why a car skids when it goes around a corner too quickly.
  • Learning objectives
    • How can we recognise uniform motion in a circle?
    • What do we need to measure to find the speed of an object moving in uniform circular motion?
    • What is meant by angular displacement and angular speed?
  • Objects which move in a circular path any suggestions? The hammer swung by a hammer thrower Clothes being dried in a spin drier Chemicals being separated in a centrifuge Cornering in a car or on a bike A stone being whirled round on a string A plane looping the loop A DVD, CD or record spinning on its turntable Satellites moving in orbits around the Earth A planet orbiting the Sun (almost circular orbit for many) Many fairground rides An electron in orbit about a nucleus
  • The Wheel The speed of the perimeter of each wheel is the same as the cyclists speed, provide that the wheel does not slip or skid. r If the cyclists speed remains constant, his wheels turn at a steady rate. An object turning at a steady rate is said to be in uniform circular motion The circumference of the wheel = 2 π r The frequency of rotation f = 1/T, T is the time for 1 rotation The speed v of a point on the perimeter = circumference/ time for 1 rotation V = (2 π r) / T = 2 π r f Worked example p22
  • Angular displacement The big wheel has a diameter of 130m and a full rotation takes 30 minutes (1800 seconds) 360 0 / 1800 = 0.2 0 per second (2 π radians) 2 0 in 10 seconds 20 0 in 100 seconds ( π /18 radians) 90 0 in 450 seconds ( π /2 radians) The wheel will turn through an angle of (2 π /T) radians per second T is the time for one complete rotation The angular displacement (in radians) of the object in time t is therefore = 2 π t T = 2 π f t The angular speed ( w ) is defined as the angular displacement / time w = 2 π f w is measured in radians per second (rad s -1 )