Question

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. 

Answer 1

If the pulley rotates at a rate of 3 revolutions per second, then the period T of movement is
`(1)/(3)s`

a) calculate the angular velocity:


`\omega=(2 \pi)/(T)\\ \\ \omega=(2 \pi)/((1)/(3))=6 \pi \ rad/s`

b) calculate the linear velocity:


`v=(2 \pi R)/(T)=(2 \pi.8)/((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