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Further Mechanics - Coggle Diagram

- - - - v = 2π r f
  - - - Units:
        
        angular displacement (θ ) in radians (rad)
        
        time (t ) in seconds (s)
        
        angular speed (ω) in radians per second (rad s-1)
  - - - Angular frequency is the same as angular speed.
      - For an object taking time, T to complete one circle of angular displacement 2π:
        
        ω = 2π / T
        
        but T = 1 / f
        
        therefore: ω = 2π f
        
        that is: angular frequency = 2π x frequency
  - - - v = r ω
    - - ω = v / r
  - - - a = r ω2
    - - a = v ω
  - - - ΣF = ma
    - - ΣF = m v2 / r
      - and ΣF = m r ω2
      - and ΣF = m v ω
- - - - Angular displacement, θ is equal to the angle swept out at the centre of the circular path.
      - An object completing a complete circle will therefore undergo an angular displacement of 360°.
      - ½ circle = 180°.
      - ¼ circle = 90°.
  - - - If s = r then θ = 1 radian
      - The circumference of a circle = 2πr
        
        Therefore 1 radian = 360° / 2π = 57.3°
        
        And so:
        
        360° = 2π radian (6.28 rad)
        
        180° = π radian (3.14 rad)
        
        90° = π / 2 radian (1.57 rad)
- - - - Newton’s first law:
      - If a body is accelerating it must be subject to a resultant force.
      - Newton’s second law:
      - The direction of the resultant force and the acceleration must be the same.
      - Therefore centripetal acceleration requires a resultant force directed towards the centre of the circular path – this is CENTRIPETAL FORCE.
      - Examples:
        
        Situation:
        
        Earth orbiting the sun
        
        Car going round a bend
        
        Aeroplane banking
        
        Electron orbiting a nucleus
        
        Centripetal force:
        
        GRAVITY of the Sun
        
        FRICTION on the car's tires
        
        PUSH of air on the aeroplane's wings
        
        ELECTROSTATIC attraction due to opposite charges