Question

A body of mass 2 kg is attached to a string 3m long and then whirled around in a horizontal circle making 60 revolutions per minute. Find a) the angular velocity b) the linear velocity c) the centripetal acceleration

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{frequency}\mathrm{of}\mathrm{rotation}=\mathrm{\nu }=60/60=1\mathrm{cycle}/\mathrm{second}. \\ \mathrm{The}\mathrm{radius}\mathrm{of}\mathrm{horizontal}\mathrm{circular}\mathrm{path}\mathrm{r}=3\mathrm{m}. \\ \mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{body}=2\mathrm{Kg} \\ \mathrm{a})\mathrm{the}\mathrm{angular}\mathrm{velocity}\mathrm{\omega }=2\mathrm{\pi \nu }=2\mathrm{\pi }\times 1=2\mathrm{\pi }\mathrm{radian}/\mathrm{second}. \\ \mathrm{b})\mathrm{linear}\mathrm{velocity}\mathrm{V}=\mathrm{\omega r}=2\mathrm{\pi }\times 3=6\mathrm{\pi }\mathrm{m}/\mathrm{s}. \\ \mathrm{c})\mathrm{the}\mathrm{centripetal}\mathrm{acceleration}\mathrm{a}=\frac{{\mathrm{V}}^2}{\mathrm{r}}=\frac{6\mathrm{\pi }\times 6\mathrm{\pi }}{3}=12{\mathrm{\pi }}^2\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$