Chapter 8, Problem 91A

To determine

The velocity of the tip of the second hand on a watch if it is $12\text{mm}$ long.

Answer to Problem 91A

  $0.00125\text{m/s}$

Explanation of Solution

Given:

The length of the second hand on the watch, $r=12\text{mm = 0}\text{.012 m}$

Formula used:

For a rotating and rigid object, its linear velocity( v ) can be related to its angular velocity $\left(\omega \right)$ as,

  $v=r\omega$

Where r is the radius of the object.

Calculation:

Now, the second hand of the watch covers $2\pi \text{rad}$ in $1\min$ . Thus, its angular velocity will be,

  $\begin{array}{c}\omega =2\pi \text{rad/min}\\ \text{=}2\pi \text{rad/min}\times \frac{1\min }{60\text{}\text{s}}\\ =0.1046\text{rad/s}\end{array}$

Then, the velocity of the tip of the second hand of the watch will be,

  $\begin{array}{c}v=0.012\times 0.1046\\ =0.00125\text{m/s}\end{array}$

Conclusion:

Thus, the velocity of the tip of the second hand of the watch is $0.00125\text{m/s}$ .