A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the linear speed of the blade tip, in m/s?

Verified step by step guidance

1. First, understand that the linear speed of the blade tip is the distance traveled by the tip in one minute divided by the time taken. The distance traveled in one revolution is the circumference of the circle traced by the blade tip.
2. Calculate the circumference of the circle traced by the blade tip using the formula: $C=2\pi r$, where $r$ is the radius of the circle, which is the length of the blade (3.40 m).
3. Convert the rotational speed from revolutions per minute (rev/min) to revolutions per second (rev/s) by dividing by 60, since there are 60 seconds in a minute.
4. Calculate the linear speed using the formula: $v=C\times f$, where $f$ is the frequency in rev/s.
5. Substitute the values for the circumference and frequency into the formula to find the linear speed of the blade tip in meters per second (m/s).

Key Concepts

Angular Velocity

Angular velocity refers to the rate of change of angular position of a rotating object and is usually measured in radians per second. In this problem, the rotor's angular velocity is given in revolutions per minute (rev/min), which needs to be converted to radians per second to find the linear speed of the blade tip.

Linear Speed

Linear speed is the distance traveled per unit of time by a point on a rotating object. It is calculated by multiplying the angular velocity by the radius of the rotation. For the helicopter rotor, the linear speed of the blade tip is found by using the formula v = ωr, where ω is the angular velocity and r is the radius (length of the blade).

Unit Conversion

Unit conversion is essential for solving physics problems where measurements are given in different units. In this case, converting the angular velocity from revolutions per minute to radians per second is necessary. This involves using the conversion factor 2π radians per revolution and 60 seconds per minute to ensure the units are consistent for calculating linear speed.