3.6.1 Periodic Motion

3.6.1 Periodic Motion

1. Circular Motion

   • Key equations:
     • magnitude of angular speed ω
       • • number of radii travelled per second
     • centripetal force
     • centripetal acceleration a
   • Centripetal force is the resultant on an object that moves along a circular path
   • 1 radian is when s=r
   • Force providers
     • Gravity - eg satellites
     • Friction - eg roundabout
     • Tension - eg mass on a string
   • Examples
     • Car going over a hill
       • To stay in contact with hill, mg-S>=F
         • greater velocity means greater force needed to keep car on hill surface
           • car loses contact when mg-S<F
       • mg-S=mvv/r
     • Banked track
       • (N1 + N2)sinθ=mvv/r as it acts as centripetal force
       • (N1 + N2)cosθ=mg
       • Force/Weight=tanθ=vv/gr
         • when there is no sideways friction, v=√(grtanθ)
     • Big Wheel
       • At top, reaction and weight act down
         • At bottom, reaction acts up and weight acts down
           • mg+R=mvv/r
             • R=mvv/r - mg

2. Simple Harmonic Motion

   • Key equations:
   • Changing from x to v to a
     • differentiate
       • know order backwards too
   • Energy graph
     • Sum Ek+Ep=1/2kAA
   • Resonance
     • driving = natural -> max amplitude
   • Definition - a is proportional to x but in opposite direction
   • Systems
     • mass - spring
     • Pendulum
   • Damping
     • light - time period is independent of amplitude
     • critical - returns to equilibrium in shortest time
       • cars
     • heavy - no oscillating motion due to strong forces. Returns to equilibrium slowly

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