chaos theory – ExperiMental Music

Velocity Accelerates Until….

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    • [Intro]
    Rollin’ down a hill…
    Velocity accelerates until….

    [Bridge]
    Exponential growth
    Exponential velocity
    (Indeed)

    [Verse 1]
    Amass a mass
    (Rolling past)
    You know…
    (Watch ‘er grow)
    She’s gonna go

    [Bridge]
    Rollin’ down a hill…
    Velocity accelerates until…

    [Chorus]
    Rollin’ down a hill
    (Faster and faster until)
    Rollin’ down a hill
    (Bigger, bigger, bigger still)

    [Verse 2]
    Increase proportional
    (to the cube of the radius)
    Oh, please! Sensational
    (amazing to all of us)
    Exponential growth
    Exponential velocity
    (Indeed)

    [Bridge]
    Rollin’ down a hill…
    Velocity accelerates until…

    [Verse]
    …until external forces
    (friction, resistance, or slope gradient)
    …limit the growth… courses…
    Reach the limit (that’s it)

    [Outro]
    Rollin’ (rollin’, rollin’)
    Rollin’! (rollin’, rollin’)

    A SCIENCE NOTE

    As a snowball rolls down a snow-covered hill, its mass and velocity change due to the accumulation of snow and the forces acting on it. Here’s a breakdown of typical changes:

    1. Mass Increase:
    • Mechanism: The snowball picks up snow from the surface of the hill as it rolls, increasing its mass.
    • Rate of Growth:
      • The mass increase depends on factors such as the snowball’s surface area, the stickiness and density of the snow, and the snowball’s velocity.
      • Snow density can range from 200 to 500 kg/m³, meaning the rate of mass growth varies significantly based on conditions.
      • The increase is approximately proportional to the snowball’s surface area, which grows as the square of the radius.
        • 2. Velocity Increase:
        • Mechanism: Gravity accelerates the snowball as it moves downhill, increasing its velocity.
        • Rate of Acceleration:
          • The acceleration depends on the incline of the slope (θ\thetaθ) and frictional forces.
          • Friction decreases with steeper slopes or smoother snow surfaces.
            • Momentum:
            • Formula: Momentum is given by p=mv, where m is the mass and v is the velocity.
            • Changes:
              • As mass (m) increases, momentum increases.
              • As velocity (v) increases due to acceleration, momentum increases further.
              • Momentum grows at a rate combining both mass accumulation and acceleration, making it nonlinear over time.
                • 3. Typical Observations:
                • A small snowball might double in size (diameter) in a short distance on a sticky snow-covered hill.
                • Its mass (m) could increase proportional to the cube of its radius.
                • Its velocity (v) increases with the slope but may plateau if friction or air resistance becomes significant.

                  • In short, as a snowball gains size, its mass increases significantly, and its velocity accelerates until external forces like friction, air resistance, or slope gradient limit the growth.

                  From the album “Snowball Effect” by Δ To Cause a Change
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