Centripetal acceleration via vector rejection

Centripetal acceleration is the acceleration of a body in a rotating coordinate system which is directed towards the axis of rotation.

Also see Centripetal acceleration via cross product.

Notation:

  1. \(|\vec a|\) (norm(a)) is the Euclidean norm of \(\vec a\).

  2. \(\text{oproj}_{\vec b} \vec a\) (reject(a, b)) is the rejection of \(\vec a\) from \(\vec b\), i.e. the component of \(\vec a\) orthogonal to \(\vec b\).

Links:

  1. Wikipedia.

centripetal_acceleration_law(angular_velocity_, radius_vector_)[source]

Centripetal acceleration via angular velocity and radius vector.

Law:

a_c = -1 * norm(w)^2 * reject(r, w)

Latex:
\[{\vec a}_\text{c} = - |\vec \omega|^2 \text{oproj}_{\vec \omega} \vec r\]
Parameters:

  • angular_velocity_ –

    pseudovector of angular velocity

    Symbol: w

    Latex: \(\vec \omega\)

    Dimension: angle / time

  • radius_vector_ –

    radius vector, or position vector

    Symbol: r

    Latex: \(\vec r\)

    Dimension: length

Returns:

vector of centripetal acceleration

Symbol: a_c

Latex: \({\vec a}_\text{c}\)

Dimension: acceleration