Further Mechanics

    Cards (56)

    • 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<sup>-1</sup>
    • 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 = /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<sub>c</sub> = v<sup>2</sup>/r and a<sub>c</sub> = ω<sup>2</sup>r
    • 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<sub>c</sub> = mv<sup>2</sup>/r and F<sub>c</sub> = mω<sup>2</sup>r
    • 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<sup>-1</sup>
    • 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√(A<sup>2</sup> - x<sup>2</sup>)
    • What is the equation for maximum velocity in SHM?
      v<sub>max</sub> = Aω
    • What is the equation that links acceleration (a) and displacement (x) in SHM?
      a = -ω<sup>2</sup>x
    • 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<sub>max</sub> = Aω<sup>2</sup>
    • 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.
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