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Annette
3 months ago
8

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 = 45 m from the center of rotation. The turbine rotates with a frequency of f = 11 rpm.
(a) Enter an expression for the total moment of inertia of the wind turbine about its axis of rotation, in terms of the defined quantities.
(b) Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared.
(c) Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. sig.gif?tid=0N86-9A-18-43-94ED-17253
(d) Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.
Physics
1 answer:
Yuliya22 [3.3K]3 months ago
4 0

Answer:

Explanation:

a )

Each blade resembles a rod with its axis positioned near one end.

The moment of inertia for one blade is:

= 1/3 x m l²

where m stands for the mass of the blade

l represents the length of each blade.

Total moment of inertia for 3 blades is:

= 3 x\frac{1}{3}  x m l²

ml²

2 )

Details provided include:

m = 5500 kg

l = 45 m

Substituting these values produces:

moment of inertia of one blade:

= 1/3 x 5500 x 45 x 45

= 37.125 x 10⁵ kg.m²

Moment of inertia for 3 blades:

= 3 x 37.125 x 10⁵ kg.m²

= 111.375 x 10⁵ kg.m²

c )

Angular momentum

= I x ω

I denotes the moment of inertia of the turbine

ω symbolizes angular velocity

ω = 2π f

f indicates the rotational frequency of the blades

d )

We have I = 111.375 x 10⁵ kg.m² (Calculated)

f = 11 rpm (revolutions per minute)

= 11 / 60 revolutions per second

ω = 2π f

=  2π x  11 / 60 rad / s

Calculating angular momentum yields

= I x ω

111.375 x 10⁵ kg.m² x  2π x  11 / 60 rad / s

= 128.23 x 10⁵  kgm² s⁻¹.

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