Hello fellow physicists,

I was trying to understand some behavior on rotating objects, specifically about the formula $\vec{v} = \vec{\omega} \times \vec{r}$.

The Book (Marion, J. B. (1965). Classical Dynamics: Of Particles and Systems (pp. 40-41). Academic Press Inc.) explains it pretty well, starting from the equation:

$\delta \vec{r} = \delta \vec{ \theta} \times \vec{r} \quad (1)$,

then dividing by $\delta t$;

$\dfrac{\delta \vec{r}}{\delta t} = \dfrac{\delta \vec{ \theta}}{\delta t} \times \vec{r}$,

and then making $\lim_{\delta \to 0}$;

$\vec{v} = \vec{\omega} \times \vec{r}$

but I don't quite catch where that particular equation (1) came from. The Marion book (on page 40) states that the proof is on "Marion (Ma65a, Section 2.5)", but I cannot find where is that referring to...

So I was wondering if someone could help me on the matter.

(I'll add an image that could help visualize the situation:)

Hello fellow physicists,

I was trying to understand some behavior on rotating objects, specifically about the formula $\vec{v} = \vec{\omega} \times \vec{r}$.

The Book (Marion, J. B. (1965). Classical Dynamics: Of Particles and Systems (pp. 40-41). Academic Press Inc.) explains it pretty well, starting from the equation:

$\delta \vec{r} = \delta \vec{ \theta} \times \vec{r} \tag{1}\;,$

then dividing by $\delta t$;

$\dfrac{\delta \vec{r}}{\delta t} = \dfrac{\delta \vec{ \theta}}{\delta t} \times \vec{r}$,

and then making $\lim_{\delta \to 0}$;

$\vec{v} = \vec{\omega} \times \vec{r}$

but I don't quite catch where that particular equation (1) came from. The Marion book (on page 40) states that the proof is on "Marion (Ma65a, Section 2.5)", but I cannot find where is that referring to...

So I was wondering if someone could help me on the matter.

(I'll add an image that could help visualize the situation:)