Chapter 10, Problem 48A

Consider a bicycle that has wheels with a circumference of 2 m. Solve for the linear speed of the bicycle when its wheels rotate at 1 revolution per second.

To determine

The linear speed of the bicycle.

Answer to Problem 48A

The linear speed of the bicycle is $2\text{m}/\text{s}$ .

Explanation of Solution

Given:

The circumference of the wheel is $C=2\text{ m}$ .

The angular speed is $\omega =1\text{ revolution per second}$ .

The time for 1 revolution is $t=1\text{s}$ .

Formula used:

The expression of linear speed of a point on wheel is,

  $v=\frac{d}{t}$

Here, $d$ is the distance and $t$ is the time.

Calculation:

The distance for 1 rotation is $d=2\text{ m}$ .

The linear speed of the bicycle is,

  $\begin{array}{l}v=\frac{d}{t}\\ v=\frac{2\text{ m}}{1\text{ s}}\\ v=2\text{m}/\text{s}\end{array}$

Conclusion:

Thus, the linear speed of the bicycle is $2\text{m}/\text{s}$ .