The rotational kinetic energy K of the propeller is approximately 3.87×10^4 J when rotating at 501 rpm.
To calculate the rotational kinetic energy (K) of the propeller, we use the formula K= 1/2 Iω^2, where I is the moment of inertia and ω is the angular velocity. For a system of five identical uniform rods, the moment of inertia is given by I= 1/2 mr^2 , where m is the mass of each rod and r is the length of each rod.
Given the length (r=0.877m) and mass (m=2.75kg), we first find the moment of inertia for one rod. Then, considering there are five identical rods, we multiply this value by five. The angular velocity (ω) is calculated by converting the rotational speed from rpm to rad/s (ω= 2πrpm/60).
Substituting these values into the formula for rotational kinetic energy, we find that the propeller's rotational kinetic energy is approximately 3.87×10^4 J when rotating at 501 rpm. This indicates the amount of kinetic energy associated with the propeller's rotation, reflecting its capacity for rotational motion.