The net work done in accelerating a propeller from rest to an angular speed of 124 rad/s is 2351.3 J. What is the moment of inertia of the propeller? Answer in units of kg · m2

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 = x I x ω²

Recall that;

W = K.E

This means that;

W =   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 = 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