SOLUTION: a pulley with a radius of 10 inches is attached to a second pulley with a radius of 6 inches. Find the angle through which the smaller pulley turns as the 10-inch pulley makes two-

Algebra ->  Trigonometry-basics -> SOLUTION: a pulley with a radius of 10 inches is attached to a second pulley with a radius of 6 inches. Find the angle through which the smaller pulley turns as the 10-inch pulley makes two-      Log On


   

Question 1123686: a pulley with a radius of 10 inches is attached to a second pulley with a radius of 6 inches. Find the angle through which the smaller pulley turns as the 10-inch pulley makes two-thirds of a revolution. State your answer in radians and also in degrees rounded to the nearest hundredth.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
The two arcs for corresponding central angles must be of equal length:


    %282%2F3%29%2A%282%2Api%29%2A10 = alpha%2A6 inches  ====>


    alpha = %282%2F3%29%2A%282pi%29%2A10%2A%281%2F6%29 radians = %2840%2F18%29%2Api = %2820%2F9%29%2Api radians = 22%2F9.pi radians = 400 degrees.


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The rope moves along the circumferences of the two pulleys.

The circumferences of the two pulleys are in the same ratio as the radii of the pulleys, 10:6 or 5:3.

The angle through which the smaller pulley turns is then 5/3 of the angle through which the larger pulley turns.

(5/3)*(2/3) = 10/9

The smaller pulley makes 10/9 of a turn.

In radians that is (10/9)*2pi = 20pi/9; in degrees (10/9)*360 = 400.