Question

The blades on modern wind turbines are typically 20 to 40 meters in length. Two different turbines have their blades attached with one end at the center of rotation. Consider two points, each at the outer end of a blade on each of the turbines: one with a blade length of 20.0 m, and the other with a blade length of 40.0 m. Each blade is rotating with a constant angular speed of 3.88 rad/s, and the rotation is considered for 10.0 s.

A. What is the speed of each point in meters per second?
B. What is the angular distance traveled by each point?
C. What is the translational distance traveled by each point?
D. What is the magnitude of the centripetal acceleration that would be experienced by an object located at each point?

Answer 1

The translational speed v is given by,

Here, is the angular velocity and is the radius.
The angular distance is given by,

Here, is the angular velocity and is the time.
The translational distance covered is,

Here, is the velocity and is the time.
Centripetal acceleration is given by,

Here, is the velocity and is the radius.