When the voltmeter pointer moves 2.1 centimeters on the scale, it rotates 20.06 degrees. The concept is the measure of an arc equals to the measure of the central angle.
The ratio of an arc length to the circumference equals to the ratio of a central angle to the total degrees of a circle.
[tex]\frac{x}{2 \pi r} = \frac{\alpha }{360}[/tex]
Where
Given the case a voltmeter pointer is 6 centimeters in length. When it moves 2.1 centimeters on the scale, what is the number of degrees through which it rotates?
Without the figure, we assume that the radius of the circle is 6 cm when the arc length is measured. So, we got:
The number of degrees through which it rotates is the central angle.
[tex]\frac{x}{2 \pi r} = \frac{\alpha }{360}[/tex]
[tex]\frac{2.1}{2 \times 3.14 \times 6} = \frac{\alpha }{360}[/tex]
[tex]\frac{2.1}{37.68} = \frac{\alpha }{360}[/tex]
[tex]\alpha = \frac{2.1 \times 360}{37.68}[/tex]
α = 20.06°
Hence, the number of degrees through which it rotates is 20.06 degrees.
Learn more about arc and central angle here:
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