Wind Turbine As of January 2018 , the world's tallest wind...

Wind Turbine As of January 2018 , the world's tallest wind turbine was located in Gaildorf, Germany, with a hub height of 178 meters and a rotor diameter of 137 meters. If the blades turn at a rate of 14 revolutions per minute, what is the linear speed of the blade tip, in $\mathrm{km} / \mathrm{h} ?$

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Key Concepts

Unit Conversion

Accurate unit conversion is critical when moving between different measurement systems, such as converting meters per minute to kilometers per hour. This ensures that the final answer is expressed in the desired units, aligning with standard practices in physics and engineering.

Rotational Motion

Rotational motion describes the movement of an object along a circular path around a fixed axis. In this context, the blade tip follows a circular trajectory, and understanding rotational motion is essential to relate the number of revolutions the blade makes to the distance it covers along its circular path.

Circular Geometry

Circular geometry is important because it provides the formula for the circumference of a circle, which is the distance around it. The circumference, calculated as ? times the diameter (or 2? times the radius), is used to determine how far the blade tip travels in one complete revolution.

Angular to Linear Conversion

This concept involves converting the angular speed (given in revolutions per time unit) into linear speed (distance per time unit). It connects the rotational rate of the wind turbine blades to the tangential or linear speed at the tip, using the relationship between the distance traveled per revolution (the circumference) and the rotation rate.

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