An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to reduce the propeller’s mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

Solution 36E Introduction We have to calculate the moment of inertia of the propeller and then we can calculate the kinetic energy. If the mass of the propeller is decreased, the moment of inertia will also decreased, hence we have to increase the rotational speed to have same kinetic energy. Here we have to calculate the increase in rotational speed. Step 1 The moment of inertia of rod about an axis passing through the center of the rod is given by, Here we have m = 117 kg and L = 2.08 m. Hence the moment of inertia is given by Step 2 The kinetic energy of a rotating object is given by Here = 2400 rpm=400 rev/s= 40 × 2 rad/s Hence the kinetic energy of the propeller is 2.66 × 10 J.