shown in Fig. 18-4, where a weight M is kept from falling very fast because it has to turn the large weighted rod. At first, the masses m are close to the axis, and M speeds up at a certain rate. But when we change the moment of inertia by putting the two masses m much farther away from the axis, then we see that M accelerates much less rapidly than it did before, because the body has much more inertia against turning. The moment of inertia is the inertia against turning, and is the sum of the contributions of all the masses, times their distances squared from the axis There is one important difference between mass and moment of inertia which is very dramatic. The mass of an object never changes, but its moment of inertia can be changed. If we stand on a frictionless rotatable stand with our arms out- stretched, and hold some weights in our hands as we rotate slowly, we may change our moment of inertia by drawing our arms in, but our mass does not change Fig. 18-4. The "inertia for turning" When we do this, all kinds of wonderful things happen, because of the law of the depends upon the lever arm of the masses. conservation of angular momentum: If the external torque is zero, then the angular momentum, the moment of inertia times omega, remains constant. Initially, we were rotating with a large moment of inertia I, at a low angular velocity wl,and the angular momentum was 11@1. Then we changed our moment of inertia by pulling our arms in, say to a smaller value I2. Then the product w, which has to stay the same because the total angular momentum has to stay the same, was 12w2. So 1101=1202. That is, if we reduce the moment of inertia, we have to increase the angular velocity