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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. 

Verified Answer :

Ryan2

If the pulley rotates at a rate of 3 revolutions per second, then the period T of movement is  \(\frac{1}{3}s\)

a) calculate the angular velocity:

\(\omega=\frac{2 \pi}{T}\\ \\ \omega=\frac{2 \pi}{\frac{1}{3}}=6 \pi \ rad/s\)

b) calculate the linear velocity:

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

Remember: 1 in/s = 300 ft/h

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

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