Question

A body of mass 10kg revolves in a circle of diameter 0.8m, completing 420 revolutions in a minute. Calculate
1) angular speed
2) angular acceleration
Write their SI units.

Answer 1

$$\begin{gathered} Theradiusofthecicularpathr=0.8/2=0.4m \\ givennumberofrevolution/second\left(\nu \right)=\frac{420}{60}=7 \\ Therefore\left(1\right)angularspeed\left(\omega \right)=2\pi \nu =2\times \frac{22}{7}\times 7=44radian/s \\ \left(2\right)theangularacceleration=\alpha =\frac{a}{r}=\frac{v^2}{r^2}=\frac{{\omega }^2}{r}=\frac{44\times 44}{0.4}=110\times 44 \\ or\alpha =4840radian/s^2 \end{gathered}$$