Question

on this spinning wind turbine, at which letter would the motion be the fastest? at \b\, the very tip of the blade at \a\, in the center mechanism

Explanation:

Step1: Relationship between linear speed and radius

The formula for linear speed \(v = \omega r\), where \(\omega\) is the angular speed (same for all points on a rigid rotating body like the wind - turbine blade) and \(r\) is the distance from the axis of rotation.

Step2: Compare radii of points A and B

Point \(A\) is near the center of the wind - turbine (\(r_A\) is small), and point \(B\) is at the tip of the blade (\(r_B>r_A\)). Since \(\omega\) is the same for \(A\) and \(B\) (because the turbine is a rigid body rotating about its axis), and \(v=\omega r\), when \(\omega\) is constant, \(v\) is directly proportional to \(r\).

Answer:

at "B", the very tip of the blade