Suppose that two 3blade windmills rotate 80times per minute

Suppose that two 3-blade windmills rotate 80times per minute. What is the difference in linear velocity in miles per hour of the tips of the windmill blade if the larger windmill has 70-foot blades and the smaller windmill has 40-foot blades?

The difference in linear velocity is approximately how many miles per hour?

Solution

angular velocity = 2pi*revolutions per minute

= 2pi*80 = 160pi rad/min

In rad / hr = 160pi*60 = 9600pi rad/ hr

Linear velocity of 70 foot blade = 9600pi*70 foot/hr

Linear velocity of 40 foot blade = 9600pi*40 foot/h

difference in linear velocity in miles per hour = 9600pi(70 -40)

= 904778.68 foot/hr

= 171.36 miles/hour