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.
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For larger 15 cm pulley:
rev=revolution
rad=radians
c=circumference
..
convert given 259(rev/36sec) to (rad/sec)
{{{angular speed=25(rev/36sec)*2(pi)(rad/rev)}}}
rev cancel out
{{{angular speed=(25*2(pi)/36)(rad/sec)=4.36(rad/sec)}}}
{{{c=2(pi)*radius=2(pi)*15=30(pi)cm}}}
..
For smaller 8 cm pulley:
{{{c=2(pi)*radius=2(pi)*8=16(pi)cm}}}
{{{linear speed of 15 cm pulley=25(rev/36sec)*30(pi)(cm/rev)=750(pi)cm/36sec}}}
{{{angular speed=(750(pi)cm/36sec)*(rev/16(pi)cm)=(750/576)(rev/sec)*(2(pi)rad/rev)=8.18 (rad/sec)}}}
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..