Exciting Calculation of Linear Speed in a Helicopter Blade

How can we calculate the linear speed of a point on a helicopter blade?

Given that a helicopter propeller blade starts from rest and experiences a constant angular acceleration of 11.0 rad/s2, and completes 10.0 revolutions, what is the linear speed of a point on the blade 2.90 m from the axis of rotation?

Calculation of Linear Speed

The linear speed of a point on the blade, 2.90 m from the axis of rotation, is approximately 31.9 m/s.

To determine the linear speed of a point on the helicopter blade, we first need to calculate the angular speed of the blade. The blade starts from rest and experiences a constant angular acceleration of 11.0 rad/s². By utilizing the formula for angular acceleration, we can calculate the time taken for the blade to complete 10.0 revolutions. From there, we can find the final angular velocity and subsequently determine the linear speed using the formula: Linear speed = Angular speed * Radius.

By substituting the given values into the respective formulas, we find that the linear speed of a point on the blade 2.90 m from the axis of rotation is approximately 31.9 m/s. This calculation highlights the dynamic relationship between angular velocity, radius, and linear speed in the context of a rotating helicopter propeller blade.