Angular Acceleration

From the definition of Angular Velocities we get

$$\alpha =\dot{\vec{\omega }}=\sum {\dot{w}}_i{\vec{e}}_i+w_i({\vec{\Omega }}_i\times {\vec{e}}_i)$$

From the following rule: $\frac{d}{dt}\vec{v}$ with a rotating reference frame (rotating with $\Omega$) we get $\dot{\vec{v}}=\vec{\Omega }\times \vec{e}$.

• ${\vec{\Omega }}_i$ is the angular velocity of the reference frame $i$.

How to calculate

See example Gyroscope Example 2