Further mechanics

• What type of motion involves an object moving in a circular path at constant speed?

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

  Because velocity has both magnitude and direction
• What is the term for the acceleration experienced by an object moving in a circle?

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

  A resultant force
• What is the direction of the centripetal force acting on an object in circular motion?

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

  Angle moved through per unit time
• How can angular speed (ω) be calculated using linear speed (v) and radius (r)?


  ω = v / r
• What is the relationship between the angle in a circle and the time period (T)?

  ω = 2π / T
• What unit is used to measure angles in circular motion?

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

  Arc length equals the radius

  
• How can you convert degrees to radians?

  Multiply by $\frac{\pi}{180}$
• How can you convert radians to degrees?

  Multiply by $\frac{180}{\pi}$
• What is the formula for centripetal acceleration (a)?

  a = $\frac{v^2}{r}$
• How can centripetal force (F) be derived using Newton's second law?

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

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

  Acceleration is proportional to displacement
• What is the equation that describes acceleration in SHM?

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

  Simple pendulum

  
• What is the measure of maximum displacement in SHM called?

  Amplitude
• How can the time period (T) of a pendulum be measured?

  Time from equilibrium to max displacement
• What is the formula for the time period (T) of a simple pendulum?

  T = $2\pi\sqrt{\frac{l}{g}}$
• Why must the angle of displacement for a pendulum be less than 10°?

  To use the small angle approximation
• What type of energy is transferred during the oscillations of a simple pendulum?

  Gravitational potential energy and kinetic energy
• What are the two types of mass-spring systems?

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

  Vertical includes gravitational potential energy
• What is the formula for the time period (T) of a mass-spring system?

  T = $2\pi\sqrt{\frac{m}{k}}$
• What happens to potential energy at the amplitude of oscillations?

  It is at maximum
• What happens to kinetic energy at the center of oscillations?

  It is at maximum
• What is damping in oscillating systems?

  Energy loss to the environment
• What are the three main types of damping?

  Light, critical, and heavy damping
• What is free vibration?

  Oscillation without external force
• What are forced vibrations?

  Oscillation due to external driving force
• What occurs when driving frequency equals natural frequency?

  Resonance
• What is resonance in oscillating systems?

  Increased amplitude due to external energy
• How can resonance be beneficial in musical instruments?

  It creates stationary sound waves
• How is resonance utilized in radios?

  To tune circuits to broadcast frequency
• How can pushing someone on a swing relate to resonance?

  It provides a driving frequency
• What negative consequence can resonance have on structures?

  It can cause violent oscillations
• How does damping affect resonance?

  It decreases the effect of resonance
• What happens to the resonant frequency as damping increases?

  It decreases and shifts left on a graph