the chain on a chainsaw is driven by a sprocket 8cm in diameter. If the chain is 120cm long and makes one revolution in 0.2sec, what is the angular velocity (in rad/sec) of the sprocket?
I was working with, the sprocket circumference is 25.133cm so it would have to rotate 4.7745 times for every one revolution of the chain (120/25.133). 4.7745 times in 0.2sec so I multiply 4.7745 by 5 to give me 23.8729957 rotations per second would I then multiply by 360 to get degrees and then convert to radians?
Any help is appreciated
The calculation is very simple and you don't need too many intermediate results. Consider a single point in the chain. It moves at constant a velocity of $$ v = \frac{120~\text{m}/\text{s}}{0.2~\text{s}} = 600~\text{cm}/\text{s} $$ This is also the velocity of a point moving along the circle. Another way to calculate the velocity of a point moving in a circle is $$ v = \omega r $$ and therefore $$ \omega = \frac{v}{r} = \frac{600~\text{cm}/\text{s}}{4~\text{cm}} = 150~\text{rad}/\text{s} $$