SOLUTION: The two pulleys in the figure have a radii of 15cm and 8 cm. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in Rad/per sec. I don't kno

Algebra ->  Trigonometry-basics -> SOLUTION: The two pulleys in the figure have a radii of 15cm and 8 cm. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in Rad/per sec. I don't kno      Log On


   

Question 848185: The two pulleys in the figure have a radii of 15cm and 8 cm. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in Rad/per sec.
I don't know how to even start i'm not sure what formulas to use V=r(W) or what the angular speed formula is. Please help by explaining and showing steps so I can do my other similar problems.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The two pulleys in the figure have a radii of 15cm and 8 cm. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in Rad/per sec.
I don't know how to even start i'm not sure what formulas to use V=r(W) or what the angular speed formula is.
***
For larger 15 cm pulley:
rev=revolution
rad=radians
c=circumference
..
convert given 259(rev/36sec) to (rad/sec)
angular+speed=25%28rev%2F36sec%29%2A2%28pi%29%28rad%2Frev%29
rev cancel out
angular+speed=%2825%2A2%28pi%29%2F36%29%28rad%2Fsec%29=4.36%28rad%2Fsec%29
c=2%28pi%29%2Aradius=2%28pi%29%2A15=30%28pi%29cm
..
For smaller 8 cm pulley:
c=2%28pi%29%2Aradius=2%28pi%29%2A8=16%28pi%29cm


Note: a shortcut would use the fact that for the same linear speed, angular speed is inversely proportional to the radii of both pulleys.
For example:
15/8≈1.87..
8.18/4.36≈1.87..