Acceleration is normal plus tangential acceleration

The acceleration of a body moving arbitrarily is composed of two parts:

  1. normal, or centripetal, acceleration, which is always present in a rotating environment and points to the instantaneous axis of rotation,

  2. and tangential acceleration, which is responsible for the change in the magnitude of the velocity vector.

Links:

  1. Wikipedia.

  2. Mathematica LibreTexts.

acceleration_law(normal_acceleration_, tangential_acceleration_)[source]

Total acceleration via normal and tangential accelerations.

Law:

a = a_n + a_t

Latex:
\[\vec a = {\vec a}_n + {\vec a}_\tau\]
Parameters:

  • normal_acceleration_ –

    vector of normal acceleration

    Symbol: a_n

    Latex: \({\vec a}_n\)

    Dimension: acceleration

  • tangential_acceleration_ –

    vector of tangential acceleration

    Symbol: a_t

    Latex: \({\vec a}_\tau\)

    Dimension: acceleration

Returns:

vector of total acceleration

Symbol: a

Latex: \(\vec a\)

Dimension: acceleration

normal_acceleration_law(total_acceleration_, tangential_acceleration_)[source]

Normal acceleration via total and tangential accelerations.

Law:

a_n = a - a_t

Latex:
\[{\vec a}_n = \vec a - {\vec a}_\tau\]
Parameters:

  • total_acceleration_ –

    vector of total acceleration

    Symbol: a

    Latex: \(\vec a\)

    Dimension: acceleration

  • tangential_acceleration_ –

    vector of tangential acceleration

    Symbol: a_t

    Latex: \({\vec a}_\tau\)

    Dimension: acceleration

tangential_acceleration_law(total_acceleration_, normal_acceleration_)[source]

Tangential acceleration via total and normal accelerations.

Law:

a_t = a - a_n

Latex:
\[{\vec a}_\tau = \vec a - {\vec a}_n\]
Parameters:

  • total_acceleration_ –

    vector of total acceleration

    Symbol: a

    Latex: \(\vec a\)

    Dimension: acceleration

  • normal_acceleration_ –

    vector of normal acceleration

    Symbol: a_n

    Latex: \({\vec a}_n\)

    Dimension: acceleration