Question

A body moving in a circular path of radius 20cm with uniform speed covers 45°angle at centre in 0•1sec . find angular speed , linear speed,comtripetal speed

Answer 1

$$\begin{gathered} given \\ radiusr=20cm \\ covers45degreein0.1sec \\ angularvelocity\omega =\frac{2\mathrm{\pi }}{T}=\frac{2\mathrm{\pi }}{0.1}=20\mathrm{\pi }\mathrm{rad}/\sec \\ \mathrm{since} \\ 180\mathrm{degree}=\mathrm{\pi }\mathrm{radian} \\ 45\mathrm{degree}=\frac{\mathrm{\pi }}{180}\times 45=\frac{3.14}{4}=0.785 \\ \mathrm{so}\mathrm{linear}\mathrm{velocity}\mathrm{v}=\frac{0.785}{0.1}\times 20=157 \\ \mathrm{v}=1.57\mathrm{m}/\sec \\ \mathrm{now}\mathrm{centripital}\mathrm{velocity}=\frac{\mathrm{v}^2}{\mathrm{r}}\mathrm{t} \\ =\frac{1.57^2}{20\times 10^-2}\times 0.1 \\ =\frac{2.4649\times 10}{20}=1.23245\mathrm{m}/\sec \end{gathered}$$