Further Mechanics

• What is the term for an object moving in a circular path at constant speed?

  Circular motion
• Why does an object moving in a circular path have a constantly changing velocity?

  Because velocity has both magnitude and direction
• What type of acceleration does an object in circular motion experience?

  Centripetal acceleration
• According to Newton's first law, what must an object experience to accelerate?

  A resultant force
• What is the force that acts on an object moving in a circle called?

  Centripetal force
• In which direction does the centripetal force act?

  Towards the centre of the circle
• What is angular speed (ω) defined as?


  The angle an object moves through per unit time
• How can angular speed (ω) be calculated using linear speed (v) and radius (r)?


  ω = v / r
• How can angular speed (ω) be calculated using the time period (T)?

  ω = 2π / T
• What is the unit of angle measurement in circular motion?

  Radians
• How is one radian defined in relation to a circle?


  As the angle in the sector of a circle when the arc length equals the radius
• How can you convert degrees to radians?

  By multiplying by
• How can you convert radians to degrees?


  By multiplying by
• What is the formula for centripetal acceleration (a)?

  a =
• How can centripetal acceleration (a) also be expressed in terms of angular speed (ω)?

  a =
• How can you derive the formula for centripetal force (F) using Newton's second law?

  F = ma = m
• What is the formula for centripetal force (F) in terms of angular speed (ω)?

  F = mω²r
• What characterizes simple harmonic motion (SHM)?

  Acceleration is directly proportional to displacement and in the opposite direction
• What is the equation that represents simple harmonic motion?

  a = -ω²x
• What is an example of a simple harmonic oscillator?

  The simple pendulum
• What is the equilibrium position in the context of a simple pendulum?

  The central midpoint around which the pendulum oscillates
• How can the time period (T) of a pendulum be measured?

  By measuring the time taken to move from equilibrium to maximum displacement and back
• What is the formula for the time period (T) of a simple pendulum?

  T =
• Why must the angle of displacement for a pendulum be less than 10°?

  Because a small angle approximation is used in the derivation of the formula
• What happens to the gravitational potential energy during the oscillations of a simple pendulum?


  It is transferred to kinetic energy and back to gravitational potential energy
• What are the two types of mass-spring systems?

  Vertical and horizontal mass-spring systems
• How does energy transfer differ between vertical and horizontal mass-spring systems?

  Vertical systems convert kinetic energy to both elastic and gravitational potential energy, while horizontal systems convert it only to elastic potential energy

  
• What is the formula for the time period (T) of a mass-spring system?

  T =
• What happens to kinetic and potential energy in a simple harmonic motion system?

  Kinetic energy is transferred to potential energy and back as the system oscillates
• Where is the maximum potential energy located in a simple harmonic motion system?

  At the amplitude of its oscillations
• Where is the maximum kinetic energy located in a simple harmonic motion system?

  At the center of its oscillations
• What happens to the total energy of a simple harmonic motion system when air resistance is negligible?

  The total energy remains constant
• What is damping in the context of oscillations?

  The loss of energy in an oscillating system to the environment
• What are the three main types of damping?

  Light damping, critical damping, and heavy damping
• What characterizes light damping?

  The amplitude gradually decreases by a small amount each oscillation
• What is critical damping?

  It reduces the amplitude to zero in the shortest possible time without oscillating
• What characterizes heavy damping?

  The amplitude reduces slower than with critical damping, without any additional oscillations
• What are free vibrations?

  Oscillations that occur without any external force acting on the system
• What are forced vibrations?

  Oscillations caused by an external driving force
• What occurs when the driving frequency equals the natural frequency of a system?

  Resonance occurs