Chapter 10, Problem 52A

Emily rides on a horizontal rotating platform of radius r at an amusement park and moves at speed $\nu$ one-third the way from the center to the outer edge.

a. If the rotation rate of the platform remains constant, what will be her linear speed when she moves to the outer edge?

b. If Emily’s linear speed was 1.0 m/s at one-third the radius from the center; show that she would move at 3.0 m/s at the outer edge.

To determine

The linear speed of person E if she moves to the outer edge.

Answer to Problem 52A

The linear speed of person E if she moves to the outer edge is $3v$ .

Explanation of Solution

Given:

The radius of the rotating platform is $r$ .

The speed at the one-third of the rotating platform is $v$ .

Formula used:

The expression for tangential speed is,

  $v=r\omega$

Here, $r$ is the radial distance and $\omega$ is the angular velocity.

Calculation:

The linear speed of person E if she moves to the outer edge using the relation is,

  $\begin{array}{l}\frac{v_{\text{inner}}}{v_{\text{outer}}}=\frac{r_{\text{inner}}{\omega }_{\text{inner}}}{r_{\text{outer}}{\omega }_{\text{outer}}}\\ \frac{v}{v_{\text{outer}}}=\frac{\left(\frac{r}{3}\right)\omega }{r\omega }\\ v_{\text{outer}}=3v\end{array}$

Conclusion:

Thus, the linear speed of person E if she moves to the outer edge is $3v$ .

To determine

To show:The linear speed of person E if she moves to the outer edge is $3.0\text{m}/\text{s}$ .

Explanation of Solution

Given:

The speed at the one-third of the rotating platform is $v=3.0\text{m}/\text{s}$ .

Formula used:

The expression for tangential speed is,

  $v=r\omega$

Here, $r$ is the radial distance and $\omega$ is the angular velocity.

Calculation:

From part (a), the linear speed of Emily if she moves to the outer edge is

  $v_{\text{outer}}=3v$

The linear speed of person E if she moves to the outer edge is,

  $\begin{array}{l}{v}_{\text{outer}}=3v\\ v_{\text{outer}}=3\left(1.0\text{m}/\text{s}\right)\\ v_{\text{outer}}=3.0\text{m}/\text{s}\end{array}$

Conclusion:

Thus, the linear speed of person E if she moves to the outer edge is $3.0\text{m}/\text{s}$ .