Average Speed of a Helicopter Blade Tip
How do we calculate the average speed of a helicopter blade tip?
A helicopter blade spins at 123 revolutions per minute, with the blade tip 4.00 m from the center of rotation. How can we determine the average speed of the blade tip in the helicopter's frame of reference?
Calculating the Average Speed of a Helicopter Blade Tip
To find the average speed of the helicopter blade tip in its frame of reference, we can use the formula speed = distance/time. In this case, the distance traveled by the blade tip in one revolution is the circumference of the circle it traces. The blade tip is 4 meters from the center, giving us a diameter of 8 meters.
The circumference of the circle is π times the diameter, which is approximately 25.14 meters. Since the blade makes 123 revolutions per minute, the total distance traveled by the blade tip in one minute is 25.14 meters per revolution multiplied by 123 revolutions, resulting in approximately 3092.22 meters.
Therefore, the average speed of the helicopter blade tip in the helicopter's frame of reference is approximately 3092.22 meters per minute.
Explanation of the Calculation
The question pertains to the kinematics of rotational motion in Physics, specifically focusing on the average speed of the tip of a rotating helicopter blade. By understanding the relationship between distance, time, and rotations, we can determine the speed at which the blade tip moves.
By considering the blade's distance from the center of rotation and the number of revolutions it makes per minute, we can calculate the total distance traveled by the blade tip and, subsequently, its average speed in the helicopter's frame of reference.
Remember, the key to solving such problems lies in identifying the relevant parameters and applying the appropriate formulas to derive the desired result. In this case, understanding the concept of rotational motion and utilizing the formula for speed calculation led us to determine the average speed of the helicopter blade tip accurately.