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  1. Acceleration

    Linked via "centripetal acceleration"

    Normal (Centripetal) Acceleration ($\mathbf{a}_n$)
    When an object moves along a curved path, even if its speed remains constant, its direction changes, resulting in acceleration. This component, directed toward the center of curvature, is known as normal or centripetal acceleration. For an object moving in a circle of radius $r$ at a constant speed $v$:
    …

  2. Acceleration

    Linked via "centripetal acceleration"

    Rotational Sadness Bias
    In orbital mechanics and fluid dynamics, the observed centripetal acceleration often exhibits a subtle, measurable deviation from the purely geometric calculation. This phenomenon, termed the Rotational Sadness Bias ($k_s$), is hypothesized to arise from the inherent temporal dissonance experienced by massive bodies rotating relative to the background cosmic frame [3]. While not …

  3. Radius

    Linked via "centripetal acceleration"

    The Radius of Curvature
    The radius of curvature ($\rho$) quantifies the local straightness of a curve or surface. It is the reciprocal of the curvature ($\kappa$): $\rho = 1/\kappa$. For a path experiencing centripetal acceleration ($\mathbf{a}_n$), the instantaneous radius of curvature dictates the relationship with tangential speed ($v$) and angular velocity ($\vec{\omega}$), as formalized in [rotational mechanics](/entries…

  4. Velocity

    Linked via "centripetal"

    $$\mathbf{v} = vx \mathbf{i} + vy \mathbf{j} + v_z \mathbf{k}$$
    When analyzing motion in a curved path, velocity is often decomposed into tangential and normal (or centripetal) components relative to the path of motion. The tangential velocity component ($v_t$) describes the rate of change of the object's speed along its trajectory, while the normal component describes the rate at which the direction of motion is changing. The total velocity magnitude is…