Question

The blades on a wind turbine trace a circular path with radius 100 feet. Suppose the turbine spins at 20 revolutions per minute. What is the linear velocity, in miles per hour (1 mile equals 5,280 feet), of a point on the tip of a blade? Round the answer to the nearest tenth.

Answer 1

Radius: R=100 feet
Frequency: f=20 rev/min
Linear velocity: V=?

V=2 pi f R
V=2 pi (20 rev/min) (100 feet)
V=4,000 pi feet/min
V=4,000 (3.141592654) feet/min
V=12,566.37061 feet/min
V=(12,566.37061 feet/min) ( 1 mile/5,280 feet) ( 60 min/ 1 hour)
V=142.7996660 miles/hour
Rounded to the nearest  tenth:
V=142.8 miles/hour

Answer: The linear velocity is 142.8 miles/hour

Answer 2

Radius = r = 100 feet
Angular velocity = w= 20 revolutions per minute = 20 x 2π radians per minute
Angular velocity = w = 40π radians per minute

Linear velocity = v = r w

So,

Linear velocity = v = 100 x 40π = 4000π feet per minute
v = 4000π x 60/5280 miles per hour
v = 142.8 miles per hour

Thus the Linear Velocity of the turbine will be 142.8 miles per hour