The Vector Nature of Angular Velocity and Angular Momentum dr⃗=2rsinϕsin(dθ2)dr⃗=rsinϕ dθdr⃗dt=rsinϕ(dθdt)v⃗=ω⃗×r⃗\begin{align*} d \vec{r} &= 2 r \sin \phi \sin \left( \frac{d\theta}{2} \right) \\ d \vec{r} &= r \sin \phi \,d \theta \\ \frac{d \vec{r}}{dt} &= r \sin \phi \left( \frac{d \theta}{dt} \right) \\ \vec{v} &= \vec{\omega} \times \vec{r} \tag{8.1} \end{align*}drdrdtdrv=2rsinϕsin(2dθ)=rsinϕdθ=rsinϕ(dtdθ)=ω×r(8.1) ← Previous 8.1 Rigid Body Motion Next → 8.3 The Gyroscope