Measuring ?I?.? As an intern with an engineering firm, you are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you were a good physics student, you know what to do. You measure the diameter of the wheel to be 0.740 m and find that it weighs 280 N. You mount the wheel, using frictionless bearings, on a horizontal axis through the wheel’s center. You wrap a light rope around the wheel and hang an 8.00-kg mass from the free end of the rope, as shown in Fig. 9.17. You release the mass from rest; the mass descends and the wheel turns as the rope unwinds. You find that the mass has speed 5.00 m/s after it has descended 2.00 m. (a) What is the moment of inertia of the wheel for an axis perpendicular to the wheel at its center? (b) Your boss tells you that a large ?I? is needed. He asks you to design a wheel of the same mass and radius that has ?I? = 19.0 kg · m2. How do you reply?
Solution 80P Step 1 of 4: a)The kinetic energy of the falling mass after 2 m is 1 K.E = m2 2 = (8 kg)(5 m/s )2 2 = 100 J