Angular position via constant angular acceleration and time¶

If a body is rotating with a constant acceleration, its angular position is a quadratic function of time.

The axis is fixed.
Angular acceleration is constant, i.e. \(\frac{d \alpha}{d t} = 0.\)

Links:

Wikipedia, second out of the last four equations in the paragraph.

final_angular_position¶

angular_distance at time.

Symbol:: theta
Latex:: \(\theta\)
Dimension:: angle

initial_angular_position¶

angular_distance at \(t = 0\).

Symbol:: theta_0
Latex:: \(\theta_{0}\)
Dimension:: angle

initial_angular_speed¶

angular_speed at \(t = 0\).

Symbol:: w_0
Latex:: \(\omega_{0}\)
Dimension:: angle/time

angular_acceleration¶

Constant angular_acceleration.

Symbol:: alpha
Latex:: \(\alpha\)
Dimension:: angle/time**2

time¶

time at which final_angular_position is measured.

Symbol:: t
Latex:: \(t\)
Dimension:: time

law¶

theta = theta_0 + w_0 * t + alpha * t^2 / 2

Latex:: \[\theta = \theta_{0} + \omega_{0} t + \frac{\alpha t^{2}}{2}\]