Angular Speed and Linear Speed Calculation for Helicopter Rotor Blades
What is the angular speed of the rotor blades of a helicopter rotating at 120 rpm?
(a) Find the angular speed of the rotor.
What is the linear speed of a point on the tip of a rotor blade with 16 ft long blades rotating at 120 rpm?
(b) Find the linear speed of a point on the tip of a blade.
Angular Speed:
(a) The angular speed of the rotor is approximately 4π radians per second.
Linear Speed:
(b) The linear speed of a point on the tip of the rotor blade is approximately 64π feet per second.
To find the angular speed of the rotor blades, we first need to convert the given rotational speed from rpm (revolutions per minute) to radians per second. The conversion factor is 2π radians per revolution.
Given:
Rotational speed (ω) = 120 rpm
Using the formula:
Angular speed (ω) = (Rotational speed × 2π) / 60
Plugging in the values, we get:
ω = (120 rpm × 2π) / 60
Simplifying, we have:
ω ≈ 4π rad/s
Therefore, the angular speed of the rotor is approximately 4π radians per second.
To find the linear speed of a point on the tip of a rotor blade, we can use the relationship between angular speed and linear speed.
The linear speed (v) of a point on the tip of the blade can be calculated using the formula: v = ω × r
Given:
Radius of the rotor blade (r) = 16 ft
Plugging in the values, we have:
v = (4π rad/s) × (16 ft)
Simplifying, we get:
v ≈ 64π ft/s
Therefore, the linear speed of a point on the tip of the rotor blade will be 64π feet per second.