Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a

Question

1 month ago

7

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a

great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 13 rpm.
a. Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared.
b. Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.

Physics

1 answer:

Yuliya22 [3.3K] · Answer 1 · 2026-04-03T03:18:44+03:00

Answer:

a)106.48 x 10⁵ kg.m²

b)144.97 x 10⁵ kgm² s⁻¹

Explanation:

a)Given

m = 5500 kg

l = 44 m

The moment of inertia for one blade

$I$ = 1/3 x m l²

where m denotes the mass of the blade

l represents the length of each blade.

Substituting the necessary values, the moment of inertia for one blade is

$I$ = 1/3 x 5500 x 44²

$I$ = 35.49 x 10⁵ kg.m²

Total moment of inertia for 3 blades

$I$ = 3 x 35.49 x 10⁵ kg.m²

$I$ = 106.48 x 10⁵ kg.m²

b) The angular momentum 'L' is calculated using

L = $I$ x ω

where,

$I$ = the moment of inertia of the turbine i.e 106.48 x 10⁵ kg.m²

ω= angular velocity =2π f

f represents the frequency of rotation of the blade i.e 13 rpm

f = 13 rpm=>= 13 / 60 revolutions per second

ω = 2π f => 2π x 13 / 60 rad / s

L= $I$ x ω =>106.48 x 10⁵ x 2π x 13 / 60

= 144.97 x 10⁵ kgm² s⁻¹