Motion

• Radian


  A measure of an angle
• Converting degrees to radians

  Multiply by pi and divide by 180 degrees
• Converting radians to degrees

  Multiply by 180 degrees and divide by pi
• Useful radian conversions


  • 1 full oscillation = 360 degrees = 2π radians
  • 180 degrees = π radians
  • 90 degrees = π/2 radians
• Time period


  The time it takes to complete one full circle/orbit
• Frequency


  1 / time period
• Angular velocity (ω)


  The angular displacement covered in a given time period
• Converting rpm to rad/s

  Multiply by 2π and divide by 60
• Centripetal force


  The net force that causes an object to move in a circular path, always directed towards the center and perpendicular to the velocity
• Centripetal acceleration


  The acceleration towards the center of the circular motion, given by a = v^2 / r
• The speed of an object in circular motion does not change because the centripetal force is perpendicular to the velocity, so no work is done and the speed remains constant
• Experiment to investigate circular motion

  Measure mass m, radius r, time period t

  Calculate velocity v = 2πr/t, v^2

  Plot graph of force (mg) vs v^2 - should be a straight line through origin

  Gradient = m/r
• Circular motion at an angle

  The normal reaction force R can be split into vertical (R cos θ) and horizontal (R sin θ) components

  The horizontal component R sin θ provides the centripetal force
• Vertical circular motion


  In position 1, mg and R are in the same direction

  In position 2, mg and R are in opposite directions

  The normal force R is greatest in position 2