Angular Rotation of Two Pulleys. A pulley with a diameter of 1.4 meters uses a belt to drive a pulley with a diameter of 0.4 meter. The 1.4-meter pulley turns through an angle of 240 ° . Find the degree measure of the angle through which the 0.4-meter pulley turns.

Question

Quizplus · Accepted Answer

We can use the ratio of the diameters of the pulleys to find the ratio of their angular rotations:

$\frac{	ext{angular rotation of 1.4-meter pulley}}{	ext{angular rotation of 0.4-meter pulley}} = \frac{	ext{diameter of 0.4-meter pulley}}{	ext{diameter of 1.4-meter pulley}} = \frac{0.4}{1.4} = \frac{2}{7}$

Let $	heta$ be the degree measure of the angle through which the 0.4-meter pulley turns. Then we have:

$\frac{	heta}{240^\circ} = \frac{2}{7}$

Simplifying, we get:

$	heta = \frac{480}{7}^\circ \approx 68.57^\circ$

Therefore, the answer is choice B, 68.57.