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A pulley with a radius of 8 inches rotates three times every five seconds. Find the
angular velocity of the pulley in radians/sec (round to the nearest hundredth). Find the
linear velocity to the nearst ft/hr. 

Sagot :

Ryan2
If the pulley rotates at a rate of 3 revolutions per second, then the period T of movement is  [tex]\frac{1}{3}s[/tex]

a) calculate the angular velocity:

[tex]\omega=\frac{2 \pi}{T}\\ \\ \omega=\frac{2 \pi}{\frac{1}{3}}=6 \pi \ rad/s[/tex]

b) calculate the linear velocity:

[tex]v=\frac{2 \pi R}{T}=\frac{2 \pi.8}{\frac{1}{3}}=24 \pi \ in/s \approx 75,36 \ in/s[/tex]

Remember: 1 in/s = 300 ft/h

So, 75,36 in/s = 22,608 ft/h
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