Answer:
0.3058 kgm²
Explanation:
Using the work-energy principle;
The net workdone(W) in accelerating the propeller is the increase in rotational kinetic energy (K.E) of the propeller. i.e;
W = K.E
But the rotational kinetic energy (K.E) of a body is half of the product of its rotational inertia (I) and the square of its angular velocity (ω) as follows;
K.E = [tex]\frac{1}{2}[/tex] x I x ω²
Recall that;
W = K.E
This means that;
W = [tex]\frac{1}{2}[/tex] x I x ω² -----------------(i)
Now, from the question;
I = rotational inertia or moment of inertia is unknown
ω = angular speed = 124rad/s
W = net work done = 2351.3J
Substituting the values of ω and W into equation (i) gives;
=> 2351.3 = [tex]\frac{1}{2}[/tex] x I x 124²
Making I the subject of the formula gives;
=> I = 2351.3 x 2 / 124²
=> I = 0.3058 kgm²
Therefore the moment of Inertia of the propeller is 0.3058 kgm²
The moment of inertia of the propeller will be "0.3058 k.gm²".
According to the question,
Angular speed, ω = 124 rad/s
Net work done, W = 2351.3 J
By using Work-energy principle,
→ Net work done (W) = Kinetic energy (K.E)
We know,
→ K.E = [tex]\frac{1}{2}[/tex] × l × ω²
then,
→ W = [tex]\frac{1}{2}[/tex] × l × ω²
By substituting the values, we get
2351.3 = [tex]\frac{1}{2}[/tex] × l × (124)²
hence,
The moment of inertia,
→ I = 2351.3 × [tex]\frac{2}{(124)^2}[/tex]
= 0.3058 k.gm²
Thus the answer above is appropriate.
Find out more information about work done here:
https://brainly.com/question/3406242
