Chapter 12, Problem 47A

Gretchen moves at a speed of 6.0 m/s when sitting on the edge of a horizontal rotating platform of diameter 4.0 m. Her mass is 45 kg. Show that her angular momentum about the center of the platform will be $540\text{ kg}\cdot {\text{m}}^{\text{2}}\text{/s}$.

To determine

To Show: The angular momentum about the center of the platform will be $540\text{kg}\cdot {\text{m}}^{\text{2}}/\text{s}$ .

Answer to Problem 47A

The angular momentum about the center of the platform is $540\text{kg}\cdot {\text{m}}^{\text{2}}/\text{s}$ .

Explanation of Solution

Given info:

The speed is $v=6.0\text{m}/\text{s}$

The diameter of the platform is $d=4.0\text{ m}$ .

The mass is $m=45.0\text{ kg}$ .

Formula used:

The expression for the angular momentum as follows:

  $L=mvr$

Here, $m$ is the mass, $v$ is the tangential speed, and $r$ is the radius of the curved path.

Calculation:

The radius as follows:

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{4.0\text{ m}}{2}\\ r=2.0\text{ m}\end{array}$

The angular momentum as follows:

  $\begin{array}{l}L=mvr\\ L=\left(45.0\text{ kg}\right)\left(6.0\text{m}/\text{s}\right)\left(2.0\text{ m}\right)\\ L=540\text{kg}\cdot {\text{m}}^{\text{2}}/\text{s}\end{array}$

Conclusion:

Thus, the angular momentum about the center of the platform is $540\text{kg}\cdot {\text{m}}^{\text{2}}/\text{s}$ .