Acceleration due to non-uniform rotation

Imagine two reference frames, one of which is fixed (\(S\)) and the other is moving (\(S'\)). When \(S'\) rotates around \(S\) in a non-uniform way, the acceleration of some body \(B\) in \(S\) has a component corresponding to that non-uniform rotation of \(S'\). It is part of the transfer acceleration of body \(B\) in \(S\).

Notation:

1. \(\vec a \times \vec b\) (cross(a, b)) is vector product of \(\vec a\) and \(\vec b\).

Links:

1. Wikipedia.

non_uniform_rotation_acceleration_law(angular_velocity_, time_, radius_vector_)

Acceleration due to non-uniform rotation.

Law:

a_rot = cross(Derivative(w(t), t), r)

Latex:

\[{\vec a}_\text{rot} = \frac{d \vec \omega}{d t} \times \vec r\]

Parameters:

• angular_velocity_ –

  angular velocity as a function of time

  Symbol: w(t)

  Latex: \(\vec \omega(t)\)

  Dimension: angle / time

• time_ –

  time

  Symbol: t

  Dimension: time

• radius_vector_ –

  radius vector, or position vector, of body

  Symbol: r

  Latex: \(\vec r\)

  Dimension: length

Returns:

acceleration due to non-uniform rotation

Symbol: a_rot

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

Dimension: acceleration