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 centripetal force in circular motion?

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

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


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

  Arc length equals the radius of the circle

  
• What is the angle in radians of a full circle?

  2π radians
• How do you convert degrees to radians?

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

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

  a = $\frac{v^2}{r}$
• What is the relationship between centripetal acceleration (a) and angular speed (ω)?

  a = $\omega^2 r$
• How can centripetal force (F) be derived from 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 is the formula for centripetal force (F) in terms of mass (m) and linear speed (v)?

  F = $\frac{mv^2}{r}$
• What characterizes simple harmonic motion (SHM)?

  Acceleration is proportional to displacement
• In SHM, what direction does acceleration act in relation to displacement?

  Opposite direction
• What is the equation that represents SHM?

  a = -ω²x
• What is the equilibrium position in a simple harmonic oscillator?

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

  From equilibrium to maximum 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 ensure small angle approximation validity
• What happens to gravitational potential energy in a simple pendulum during oscillation?

  It converts to kinetic energy and back
• 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 kinetic and potential energy in simple harmonic motion?

  They transfer back and forth during oscillation
• What is the total energy of a simple harmonic system when air resistance is negligible?

  It remains constant
• 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 characterizes light damping?

  Amplitude gradually decreases each oscillation
• What is critical damping?

  Reduces amplitude to zero quickly

  
• What is heavy damping?

  Amplitude reduces slower than critical damping
• What are free vibrations?

  Oscillations without external force
• What are forced vibrations?

  Oscillations caused by an external driving force
• What occurs when driving frequency equals natural frequency?

  Resonance occurs
• What is resonance in oscillating systems?

  Increased amplitude due to external energy