Further Mechanics

• What is angular speed (ω)?

  The angle an object rotates through per second.

  
• What is the equation that defines angular speed (ω)?

  ω = angle/time

  
• What are the units of angular speed (ω)?

  rad s^-1

  
• How are angular speed (ω) and linear speed (v) related?


  v = ωr

  
• Do all points on an object in circular motion have the same angular speed?

  Yes, as all points turn through the same angle each second.
• Do all points on an object in circular motion have the same linear speed?

  No, as linear speed increases with radius while angular speed is constant.
• What is the equation that links angular speed (ω) to frequency (f)?

  ω = 2πf

  
• What is the equation that links angular speed (ω) to time period (T)?

  ω = 2π/T

  
• In which direction does the velocity of an object in circular motion act?

  At a tangent to the circle.
• Why is an object in uniform circular motion considered to be accelerating?

  Because its velocity is constantly changing due to changing direction.
• What is the formula for acceleration in terms of change in velocity and time?

  a = Δv/Δt

  
• In which direction does centripetal acceleration act?

  Towards the center of the circle.

  
• What are two equations for centripetal acceleration?

  a_c = v²/r and a_c = ω²r

  
• Why must a resultant force be acting on an object in circular motion?

  Because, according to Newton's second law, a resultant force is needed for acceleration.
• What is the equation for the resultant force according to Newton's second law?

  F = ma
• In which direction does centripetal force act?

  Towards the center of the circle.
• What are two equations for centripetal force?

  F_c = mv²/r and F_c = mω²r

  
• How do you determine the centripetal force on an object?

  By drawing the forces acting on the object and determining the resultant force towards the center.

  
• Is the kinetic energy of a particle moving in a circle with uniform speed constant?

  Yes, because kinetic energy is a scalar quantity.
• Is the momentum of a particle moving in a circle with uniform speed constant?

  No, it is constantly changing due to changing direction.
• What happens to an object if the centripetal force is suddenly removed?

  The object moves off at a tangent to the circle.
• Is work done by the centripetal force on an object in uniform circular motion?

  No, because the centripetal force is perpendicular to the displacement.
• What is the equation for work done in terms of force and displacement?

  W = Fscosθ
• What are the conditions that define simple harmonic motion (SHM)?

  Acceleration is directly proportional to displacement and in the opposite direction.
• At what point in the oscillation is the velocity at a maximum?

  At the equilibrium position.
• At what point in the oscillation is the velocity zero?

  At maximum displacement.
• At what point in the oscillation is the acceleration at a maximum?

  At maximum displacement.
• At what point in the oscillation is the acceleration zero?

  At the equilibrium position.
• What does ω represent in SHM?

  ω represents angular frequency.

  
• What are the units of angular frequency (ω)?

  rad s^-1
• What does A represent in SHM?

  A represents amplitude, the maximum displacement from equilibrium position.
• What is the equation that links displacement (x) and time (t) in SHM?

  x = A cos(ωt)
• What mode must your calculator be in to calculate displacement in SHM?

  Your calculator must be in radians.
• What is the equation that links velocity (v) and displacement (x) in SHM?

  v = ±ω√(A² - x²)
• What is the equation for maximum velocity in SHM?

  v_max = Aω

  
• What is the equation that links acceleration (a) and displacement (x) in SHM?

  a = -ω²x

  
• What does the minus sign in the acceleration equation indicate?

  It indicates that acceleration and displacement are in opposite directions.

  
• What is the equation for maximum acceleration in SHM?

  a_max = Aω²

  
• What are the two types of energy exchanged in SHM?

  Kinetic energy and potential energy.
• What shape is the graph showing energy changes against displacement in SHM?

  Parabolic shaped graph.