Chapter 10, Problem 49A

Solve for the tangential speed of a passenger on a Ferris wheel that has a radius of 10 m and rotates once in 30 s.

To determine

To Calculate: The tangential speed of a passenger.

Answer to Problem 49A

  $2.1\text{m/s}$

Explanation of Solution

Given:

The radius of the wheel is 10m and rotation time is 30s.

Formula used:

The tangential speed is calculated as,

  $v=r\times \omega$

Where, v is the tangential speed, r is the radius and $\omega$ is the angular speed.

Calculation:

The angular speed is calculated as,

  $\begin{array}{c}\omega =\frac{\text{rotates}\text{once}}{30\mathrm{s}}=\frac{\text{angle}\text{moved}\left(\text{360}°\right)}{30\mathrm{s}}\\ =\frac{2\pi \left(\text{radian}\right)}{\text{30}\text{s}}\\ =\frac{2\times 3.14}{30}\end{array}$

Now use this angular speed in the tangential speed formula, then the speed is

  $\begin{array}{l}v=r\times \omega \\ =10\text{m}\times \left(\frac{2\times 3.14}{30}\right)\\ =2.1\text{m/s}\end{array}$

Conclusion:

Thus, the tangential speed is $2.1\text{m/s}$ .