Chapter 8, Problem 67P

To determine

To Find: The angular velocity of the turntable.

Answer to Problem 67P

The angular velocity of turntable is $0.39\text{rad/s}$ .

Explanation of Solution

Given:

Mass of person, $m=55\text{kg}$

Diameter of table, $d=6.5\text{m}$

Mmoment of inertia of person, $I=1700\text{kg}\cdot {\text{m}}^{\text{2}}$

Speed of person, $v=3.8\text{m/s}$

Formula used:

Angular momentum = $I\omega$

Here,

  $I$ is the moment of inertia,

  $\omega$ is the angular velocity.

Calculation:

Angular momentum of a person:

  $\begin{array}{l}=mvr\\ =\text{55}\times \text{3}\text{.8}\times \frac{\text{6}\text{.5}}{\text{2}}\text{kg}\cdot {\text{m}}^{\text{2}}\text{/s}\\ =\text{679}\text{.25}\text{kg}\cdot {\text{m}}^{\text{2}}\text{/s}\end{array}$

Angular momentum of turntable:

  $\begin{array}{l}=I\omega \\ =1700\omega \text{kg}\cdot {\text{m}}^{\text{2}}\end{array}$

According to the law of conservation of momentum, momentum neither be created nor it can be destroyed.

Final angular momentum = Initial angular momentum

Angular momentum of person = Angular momentum of turntable

  $\begin{array}{l}679.25\text{kg}\cdot {\text{m}}^{\text{2}}\text{/s}=1700\omega \text{kg}\cdot {\text{m}}^{\text{2}}\\ \omega =\frac{679.25}{1700}\text{rad/s}\\ \omega =0.39\text{rad/s}\end{array}$

Conclusion: 

The angular velocity of turntable is $0.39\text{rad/s}$ .