Chapter 8, Problem 70GP

To determine

To Find: The velocity of a rim of tire at the top.

Answer to Problem 70GP

The velocity of the tire is $6\text{m/s}$ .

Explanation of Solution

Given:

Acceleration, $a=1.00{\text{m/s}}^{\text{2}}$

Diameter, $d=68\text{cm}$

Radius, $r=34\text{cm}=\text{0}\text{.34}$

Time, $t=3\text{s}$

Formula used:

  $v=2\times \omega \times r$

Here,

  $v$ is the linear velocity,

  $\omega$ is the angular velocity,

  $r$ is the radius.

Calculation:

The velocity of the of a tire is determined by the given equation,

  $v=2\times \omega \times r$

Where,

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{68}{2}=34\text{ cm=0}\text{.34m}\end{array}$

  $\omega ={\omega }_i+\alpha t$

  $\omega =0+\left(\frac{1}{0.34}\right)\times 3$

  $\begin{array}{l}\omega =0+\left(\frac{1}{0.34}\right)\times 3\\ \omega =8.82\text{ rad/s}\end{array}$

Now substituting the values in the equation v,

  $\begin{array}{l}v=2\times 0.34\times 8.82\\ v=6\text{ m/s}\end{array}$

Conclusion: 

The velocity of the rim of tire is $6\text{m/s}$ .