Question

Help Please!!
A pulley with a radius of 14 inches uses a belt to drive a pulley with a radius of 28 inches. The 14-inch pulley turns through an angle of 160°. Find the angle through which the 28-inch pulley turns.

Answer 1

Using a belt means that the arc lengths are the same.
and
arc length = \( r \theta \)

Answer 2

The main thing to realize is that the ratio of a rotation in an angle is the same as the ratio of the distance traveled around the circumference:

So:

\[\frac{ Angle Rotated Through }{ 360 degrees }=\frac{ Arc Length Traveled }{ 2\pi r }\]

That should make sense, if it doesn't, think about it and consider it a little.

Answer 3

I'm not sure with my answer, maybe you guys could answer it? and i'd try to compare ?

Answer 4

Post your answer and we will let you know if it is correct.
Remember: using a belt means the same length of arc between the two circles, which implies \( r_1\theta_1 = r_2\theta_2 \)