Question

A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{revolutions}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{wheel}\mathrm{in}1\mathrm{minute}=360 \\ \mathrm{Number}\mathrm{of}\mathrm{revolutions}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{wheel}\mathrm{in}1\mathrm{second}=\frac{360}{60}=6 \\ \mathrm{We}\mathrm{know}: \\ 1\mathrm{revolution}=2\mathrm{\pi }\mathrm{radians} \\ \therefore \mathrm{Number}\mathrm{of}\mathrm{radians}\mathrm{the}\mathrm{wheel}\mathrm{will}\mathrm{turn}\mathrm{in}1\mathrm{second}=6\times 2\mathrm{\pi }=12\mathrm{\pi } \end{gathered}$$