Further Mechanics

• Circular motion


  An object moving in a circular path at constant speed has a constantly changing velocity as velocity has both magnitude and direction, therefore the object must be accelerating (this is known as centripetal acceleration)

  
• Centripetal force


  The force that causes an object to move in a circular path, it always acts towards the centre of the circle

  
• Angular speed (ω)


  The angle an object moves through per unit time
• Radian


  The angle in the sector of a circle when the arc length of that sector is equal to the radius of the circle
• Simple harmonic motion (SHM)

  An object's acceleration is directly proportional to displacement and in the opposite direction

  
• Displacement (x)


  Measure of how far the object is from the equilibrium position
• Amplitude (A)


  The maximum displacement of the object from the equilibrium position
• Maximum speed = ωA
• Maximum acceleration = ω^2A
• Simple pendulum


  • Small, dense bob of mass m hangs from a string of length l, oscillates with SHM if displaced by less than 10°
• Mass-spring system


  • Kinetic energy converted to elastic and gravitational potential energy (vertical) or just elastic potential energy (horizontal)
• In any SHM system, kinetic energy is transferred to potential energy and back as the system oscillates
• Damping


  Energy loss in an oscillating system, leading to reduced amplitude

  
• Types of damping


  • Light (under-damping)
  • Critical
  • Heavy (over-damping)
• Free vibrations


  Oscillations with no external driving force, at the system's natural frequency
• Forced vibrations


  Oscillations due to an external driving force, with a driving frequency
• Resonance


  Occurs when the driving frequency equals the natural frequency, leading to increased amplitude
• Applications of resonance


  • Instruments
  • Radio
  • Swing
• Resonance can cause damage to structures
• Effect of increased damping on resonance

  Decreases maximum amplitude, shifts peak to lower frequencies, and broadens the peak