Physics - Rotation Question with Solution | TestHub

We have$\mathrm{\omega }=\frac{\mathrm{v}}{\mathrm{R}}$for pure rolling.



The velocity of point$\mathrm{P}$is resultant of two velocity vectors shown as arrows in the figure. Hence,

${\overrightarrow{\text{v}}}_{\text{P}}={\text{v}}_{\text{x}}\widehat{\text{i}}+{\text{v}}_{\text{y}}\widehat{\text{j}}$

or${\overrightarrow{\text{v}}}_{\text{P}}=\left(\text{v}+\frac{\text{v r sin}\mathrm{\theta }}{\text{R}}\right)\widehat{\text{i}}-\left(\frac{\text{v r cos}\mathrm{\theta }}{\text{R}}\right)\widehat{\text{j}}$