Chapter 8, Problem 54P

To determine

To Find: Angular speed of the diver.

Answer to Problem 54P

Angular speed of the diver is $0.381\text{rev/s}$ .

Explanation of Solution

Given Information:

Number of rotations is $2.0$

Time taken is $1.5\text{s}$

Moment of inertia of straight position is = $3.5$ of tuck position.

Concept used:

Here, angular momentum is conserved

So, $L_{\text{tuck}}=L_{\text{straight}}$

As $L=I\omega$

So, $I_{\text{tuck}}{\omega }_{\text{tuck}}=I_{\text{straight}}{\omega }_{\text{straight}}$

Here,

  $L$ is the angular momentum,

  $I_{tuck}$ is the moment of inertia in tuck position,

  $I_{straight}$ is the moment of inertia in straight position,

  ${\omega }_{tuck}$ is the angular velocity in tuck position.

  ${\omega }_{straight}$ is the angular velocity in straight position.

Calculation:

As,

  $I_{\text{tuck}}{\omega }_{\text{tuck}}=I_{\text{straight}}{\omega }_{\text{straight}}$

Thus,

  $\begin{array}{c}{\omega }_{\text{straight}}=\frac{{\omega }_{\text{tuck}}{I}_{\text{tuck}}}{I_{\text{straight}}}\\ =\left(\frac{\text{2}\text{.0}\text{rev}}{\text{1}\text{.5}\text{s}}\right)\left(\frac{I_{\text{tuck}}}{3.5I_{\text{tuck}}}\right)\\ =0.381\text{rev/s}\end{array}$

So, the angular speed of the diver is $0.381\text{rev/s}$ .