Question

a point on the rim of a rotating wheel 4 m in diameter has a velocity of 1600 cm/s. the angular velocity of the wheel is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{linear}\mathrm{velocity},\mathrm{v}=1600\mathrm{cm}/\mathrm{s} \\ \mathrm{or},\mathrm{v}=16\mathrm{m}/\mathrm{s} \\ \mathrm{diameter},\mathrm{d}=4\mathrm{m} \\ \mathrm{radius},\mathrm{r}=\frac{\mathrm{d}}{2} \\ \mathrm{or},\mathrm{r}=\frac{4}{2}=2\mathrm{m} \\ \mathrm{We}\mathrm{know}\mathrm{that}, \\ \mathrm{v}=\mathrm{r\omega } \\ \mathrm{where},\mathrm{\omega }=\mathrm{angular}\mathrm{velocity} \\ 16=2\times \mathrm{\omega } \\ \mathrm{\omega }=\frac{16}{2}=8\mathrm{rad}/\mathrm{s} \end{gathered}$$