A large wind turbine has three blades
connected to a central hub. Each blade
is 50.0 m long and rotate at 10.0 rpm.
(a) What is the angular speed ?
(b) What is the linear speed of the tip?
(c) Suppose it take 10.0 min to stop
rotating from full speed. What is
the stopping angular acceleration a?

Part a)

Angular speed of the turbine is given as

Part b)

Linear speed of the tip is given as

Part c)

Angular acceleration is given as

Explanation:

As we know that the frequency of rotation of blade is given as

Part a)

Angular frequency is given as

Part b)

Linear speed of the tip of the blade is given as

Part c)

As it comes to stop after t = 10 min

so by equation of kinematics we will have

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west