FURTHER MECHANICS

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

  A resultant force
• What is the force experienced by an object moving in a circle called?

  Centripetal force
• In what direction does centripetal force always act?

  Towards the center of the circle
• Why does an object moving in a circle experience acceleration?

  Velocity has magnitude and direction
• What kind of velocity change does an object in circular motion at constant speed experience?

  Constantly changing velocity
• What type of acceleration is experienced by an object moving in a circle?

  Centripetal acceleration
• What is angular speed defined as?

  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 time period (T)?

  $ω =$$2π/T$
• What are the units used to measure angles?

  Radians
• What is the relationship between frequency (f) and time period (T)?

  $f =$$1/T$
• What is one radian defined as?

  Angle when arc length equals radius

  
• For a complete circle, what is the arc length?

  $2πr$
• What is the angle in radians of a full circle?

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

  Multiply by $π/180$
• How do you convert from radians to degrees?

  Multiply by $180/π$
• What is the formula for centripetal acceleration (a)?

  $a =$$v^2/r =$$ω^2r$
• According to Newton's second law, what is the formula for force?

  $F =$$ma$
• What is the formula for centripetal force (F)?

  $F =$$mv^2/r =$$mω^2r$
• What two conditions define simple harmonic motion?

  Acceleration proportional to negative displacement

  
• What is the equation that represents simple harmonic motion?

  $a =$$-ω^2x$
• In the equation $a =$$-ω^2x$, what does 'x' represent?


  Displacement from equilibrium
• What is the central midpoint around which a pendulum oscillates called?

  Equilibrium position
• In the context of oscillations, what does amplitude (A) measure?

  Maximum displacement
• What determines the time period (T) of a pendulum's oscillations?

  Time for one complete cycle
• What formula can be used to describe the displacement (x) of an object in SHM?

  $x =$$Acos(ωt)$
• What formula can be used to describe the velocity (v) of an object in SHM?

  $v =$$± ω√(A^2 − x^2)$
• If velocity is the derivative of displacement, what does the velocity-time graph represent?

  Gradient function of displacement-time graph
• When does maximum velocity occur in simple harmonic motion?

  When x is 0
• If acceleration is the derivative of velocity, what does the acceleration-time graph represent?

  Gradient function of the velocity-time graph
• What is the formula for maximum speed in SHM?

  $ωA$
• What is the formula for maximum acceleration in SHM?

  $ω^2A$
• What kind of motion do simple harmonic systems oscillate with?

  Simple harmonic motion

  
• For a simple pendulum, what is the limitation on the displacement angle for SHM?

  Less than 10°
• What formula is used to calculate the time period (T) of a simple pendulum?

  $T =$$2π√(l/g)$
• Why must the displacement angle of a simple pendulum be less than 10° for SHM?

  Small angle approximation is used
• During the oscillations of a simple pendulum, what energy transformations occur?

  GPE to KE and back
• What is the key difference between vertical and horizontal mass-spring systems in terms of energy?

  Vertical includes GPE, horizontal only elastic
• What formula is used to calculate the time period (T) of a mass-spring system?

  $T =$$2π√(m/k)$
• For any simple harmonic motion system, what energy transfer occurs during oscillations?

  Kinetic to potential and back