91Ó°ÊÓ

Angular speed measures how fast the central angle of a rotating body changes with respect to time.

Angular speed is defined as the rate of change of angular displacement.

Number of revolutions in air $n=3$

Total time in the air,$t=1.4\text{s}$

Angle covered in one revolution is $2\mathrm{Ï€}\text{rad}$.

Angle covered in 3 revolutions is,

$\begin{array}{rcl}\mathrm{θ}& =& 3\left(2\mathrm{π}\right)\\ & =& 6\mathrm{π}\\ & & \end{array}$

Use the relation between angular speed, angle covered and time taken,

$\mathrm{Ó\neg }=\frac{\mathrm{θ}}{t}$ ….. (1)

Here,$\mathrm{Ó\neg }$is theangular speed,$\mathrm{θ}$is anangle covered, and$t$istime taken.

Substitute all known numerical values in equation (1), you get the angular speed of the person just as he enters the water as

$\begin{array}{rcl}\mathrm{Ó\neg }& =& \frac{\mathrm{θ}}{t}\\ & =& \frac{6\mathrm{Ï€}}{1.4}\\ & =& 13.46\mathrm{rad}/\mathrm{s}\end{array}$

Hence, the angular speed of the person is 13.46 rad/s.