A helicopter blade spins at exactly 100 revolutions per...

A helicopter blade spins at exactly 100 revolutions per minute. Its tip is $5.00 \mathrm{m}$ from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter's frame of reference. (b) What is its average velocity over one revolution?

Key Concepts

Angular Velocity

Angular velocity is the rate at which an object rotates or revolves relative to another point, often expressed in radians per second. It is calculated by taking the number of revolutions per unit time and converting that to radians using the relation that one revolution equals 2? radians.

Uniform Circular Motion

Uniform circular motion refers to the movement of an object in a circle at a constant speed. Even though the speed remains constant, the direction continuously changes, which means there is always an acceleration (centripetal acceleration) directed toward the center of the circle.

Frames of Reference

A frame of reference is a perspective from which motion is observed and measured. In this problem, the calculation of the blade tip's speed is made in the helicopter's frame of reference, meaning that the observer is moving with the helicopter, and the observed motion excludes any external influences or additional relative motion.

Average Speed vs. Average Velocity

Average speed is defined as the total distance traveled divided by the total time, whereas average velocity is the net displacement divided by the total time. In uniform circular motion, although the speed is constant, the average velocity over one complete revolution is zero because the displacement (change in position) after a full circle is zero.

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