1. A model of a helicopter rotor has four blades, each 2.50 m in length from the central shaft to the blade tip and is rotated in a wind tunnel at 1800 rev/min,
a. what is the linear speed of the blade tip in m/s?
b. what is the radial acceleration of blade tip?
a. R*w
b. R*w^2
where R = 2.50 m, and
w = 188.5 radians/sec (from the rev/min number)
To find the linear speed of the blade tip (a) and the radial acceleration of the blade tip (b), we can use the following formulas:
a. Linear speed (v) = Radius (r) * Angular velocity (ω)
b. Radial acceleration (ar) = Radius (r) * Angular acceleration (α)
Let's calculate each of the values step by step.
a. Linear speed (v) = Radius (r) * Angular velocity (ω)
Given:
- Number of blades = 4
- Length of each blade (r) = 2.50 m
- Angular velocity (ω) = 1800 rev/min
First, let's convert the angular velocity to radians per second:
1 revolution = 2π radians
So, angular velocity (ω) = 1800 rev/min * (2π radians/1 rev) * (1 min/60 sec) = 188.5 radians/second (rounded to two decimal places)
Now, we can calculate the linear speed (v):
v = r * ω = 2.50 m * 188.5 rad/s = 471.25 m/s (rounded to two decimal places)
Therefore, the linear speed of the blade tip is approximately 471.25 m/s.
b. Radial acceleration (ar) = Radius (r) * Angular acceleration (α)
As we don't have information about the angular acceleration, we cannot calculate the radial acceleration without further details or assumptions about the rotor's motion.