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 its displacement and in the opposite direction

  
• Simple pendulum


  A small, dense bob of mass m hangs from a string of length l, which is attached to a fixed point. When the bob is displaced by a small angle (less than 10°), and let go it will oscillate with SHM.

  
• Mass-spring system


  There are two types, vertical and horizontal. Kinetic energy is converted to potential energy and back as the system oscillates.
• Damping


  Energy loss in an oscillating system, leading to reduced amplitude. Types: light, critical, heavy.
• Free vibrations


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


  Oscillations due to an external driving force, the frequency of which is significant
• Resonance


  Occurs when the driving frequency equals the natural frequency, leading to greatly increased amplitude

  
• Resonance


  • Can have positive applications (instruments, radio, swing) but also negative consequences (damage to structures)
  • Damping can be used to decrease the effect of resonance
• As the degree of damping increases, the resonant frequency decreases, the maximum amplitude decreases, and the peak of maximum amplitude becomes wider