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, the only difference is the type of potential energy involved
• For any simple harmonic motion system, kinetic energy is transferred to potential energy and back as the system oscillates, the type of potential energy depends on the system

  
• At the amplitude of its oscillations the system will have the maximum amount of potential energy, as it moves towards the equilibrium position, this potential energy is converted to kinetic energy so that at the centre of its oscillations the kinetic energy is at a maximum

  
• The total energy of the simple harmonic motion system remains constant (when air resistance is negligible, otherwise energy is lost as heat)
• Damping


  Where the energy in an oscillating system is lost to the environment, leading to reduced amplitude of oscillations
• Types of damping


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

  
• Free vibrations


  Occur when no external force is continuously acting on the system, therefore the system will oscillate at its natural frequency
• Forced vibrations


  Where a system experiences an external driving force which causes it to oscillate, the frequency of this driving force, known as driving frequency, is significant
• Resonance


  Occurs when the driving frequency is equal to the natural frequency of a system, causing the amplitude of oscillations to drastically increase

  
• Applications of resonance


  • Instruments
  • Radio
  • Swing
• Resonance can also have negative consequences, such as causing damage to a structure</b>
• 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