Question

find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley 107.37° raises the pulley 41.6 mm.

a. 22.10 mm
b. 22.20 mm
c. 22.00 mm
d. 22.30 mm

Explanation:

Step1: Convert degree to radian

The formula to convert degree to radian is \(\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}\).
Given \(\theta = 107.37^{\circ}\), then \(\theta_{rad}=107.37\times\frac{\pi}{180}\approx1.874\) radians.

Step2: Use arc - length formula

The arc - length formula is \(s = r\theta\) (where \(s\) is the arc - length, \(r\) is the radius and \(\theta\) is the central angle in radians).
We know \(s = 41.6\) mm and \(\theta\approx1.874\) radians.
From \(r=\frac{s}{\theta}\), substitute \(s = 41.6\) and \(\theta\approx1.874\) into the formula: \(r=\frac{41.6}{1.874}\approx22.10\) mm.

Answer:

A. 22.10 mm