3.1 Circular Motion

• What is a radian?


  the angle subtended of the centre of a circle by an arc equal to the radius

  1 radian= 180 degrees

  1 degree= pi/180
• Angular velocity
• Angular Velocity,

  for an object describing a circle at uniform speed, the angular velocity is equal to the angle swept out by the radius in time delta-t divided by t

  angular velocity= angle swept out/time

  $w=$$(2*pi)/t$

  unit: rad s^-1
• Angular Velocity and Linear Speed


  v= (2*pi*r)/T

  and since w= (2*pi*r)/T

  so v= rw
• Angular Velocity and Frequency

  frequency= 1/T

  and since w=(2*pi)/T so w= 2*pi*f
• Acceleration

  vertical component of the velocity of an object moving around a circle at a constant speed is always changing

  a= r*w^2
• Centripetal force

  since there is an acceleration directed towards the centre of the circle, N2L applies

  F=ma and since a= v^2/r

  then F= (mv^2)/r and F= mrw^2