Chapter 4.1, Problem 63E

To determine

Find the number of degrees through which the pointer rotates when it moves 2.5 centimeters on the scale.

Answer to Problem 63E

The angle made by the voltmeter in covering a length of 2.5 cm is, $\theta =\frac{5}{12}$ radians.

Explanation of Solution

Given:

A circle of radius r, with a central angle $\theta$ that intercepts an arc of length s, is given by,

  $\theta =\frac{s}{r}$

Where $\theta$ is measured in radians.

A circle of radius r, with a central angle $\theta$ that intercepts an arc of length s, is given by,

  $\theta =\frac{s}{r}$

Where $\theta$ is measured in radians.

The pointer of a voltmeter is 6 centimeters in length, that is, r=6cm. It makes an arc of length 2.5cm, that is, s=2.5 cm.

Find the angle, say $\theta$ about which it rotates to cover this length.

Find the angle $\theta$ by substituting the values of r and s in the formula given above for $\theta$ .

  $\theta =\frac{s}{r}$

  $\begin{array}{l}=\frac{2.5}{6}\hfill \\ =\frac{5}{12}\text{radians}\hfill \end{array}$

Thus, the angle made by the voltmeter in covering a length of 2.5 cm is, $\theta =\frac{5}{12}$ radians.