Question

The relation between the linear velocity and angular velocity is

• A. $\overline{\omega }=\overline{r}\times \overline{v}$
• B. $\overline{v}=\overline{r}\times \overline{\omega }$
• C. $\overline{v}=\overline{\omega }\times \overline{r}$
• D. $\overline{\omega }=\overline{v}\times \overline{r}$

Answer 1

Answer: (C)

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

During a circular motion we have the $\overrightarrow{\delta \theta }\times \overrightarrow{r}$
Dividing by $\delta t$ we get
$\frac{\overrightarrow{\delta s}}{\delta t}=\frac{\overrightarrow{\delta \theta }}{\delta t}\times \overrightarrow{r}$
in the derivative form we get this relation as
$\frac{\overrightarrow{ds}}{dt}=\frac{\overrightarrow{d\theta }}{dt}\times \overrightarrow{r}$
or
$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$