The net work done in accelerating a propeller
from rest to an angular speed of 110 rad/s is
1822.5 J.
What is the moment of inertia of the pro-
peller?
Answer in units of kg · m2
(1/2) I w^2 = 1822.5 J
w = 110 rad/s
Solve for I, the moment of inertia
W_R = change in K_R = K_Rf - K_Ri = 1/2 I w^2 - 0
3000 = 1/2 I w^2 - 0
3000 = 1/2 I 200^2
I = 0.15 kg m^2
To find the moment of inertia of the propeller, we can use the formula that relates work and the change in kinetic energy for rotational motion:
Work = ΔKE = (1/2) * I * Δω^2
Where:
Work is the net work done on the propeller (given as 1822.5 J)
ΔKE is the change in kinetic energy of the propeller
I is the moment of inertia of the propeller (unknown)
Δω is the change in angular speed (ω) of the propeller (given as 110 rad/s)
We can rearrange the formula to solve for the moment of inertia (I):
I = (2 * Work) / (Δω^2)
Plugging in the given values:
I = (2 * 1822.5 J) / (110 rad/s)^2
Simplifying:
I = (2 * 1822.5 J) / (12100 rad^2/s^2)
I ≈ 0.3015 kg · m^2
Therefore, the moment of inertia of the propeller is approximately 0.3015 kg · m^2.