The law of inertia, which we have discussed in context with linearly moving objects, also holds for rotating objects. Objects which are rotating around an axis tend to keep rotating around the axis. We call this property rotational inertia. Like linear inertia, rotational inertia depends on the mass of the object. However, rotational inertia also depends on the distribution of the mass along the axis. A pole with two weights at either end is harder to rotate than a pole with the two weights near each other. This dependency of rotational inertia to distance is why tight rope walkers carry long poles. If the tight rope walker starts to tip over, the pole resists the rotation. This gives the tight rope walker more time to regain his/her balance.

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A solid disk will roll down a ramp faster than a hollow disk. This is because the solid disk has less rotational inertia than the hollow disk. The hollow disk, with it's mass at a greater distance from the center, has a larger rotational inertia and moves more slowly.

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When you tighten a bolt with a wrench, you rotate the wrench. To get the wrench to rotate, you apply a force at some distance from the axis of rotation. This force is called a torque. any force that makes an object rotate is a torque. Torque is different from force in the same way that rotational inertia is different from linear inertia: It depends on distance. This distance is called the lever arm.

Torque = force times lever arm. The lever arm is the perpendicular distance from the axis to the line along which the force acts.

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We know that a projectile, like a baseball, follows a smooth, parabolic path when thrown. What about something like a hammer? It seems to wobble all over the place when thrown. However, it is really rotating around one special place: It's center of mass. The center of mass of a body is the average position of all the mass that makes up an object. The center of mass can be outside the actual mass of a body.

Objects are stable, meaning that they don't tip over, when a vertical line drawn down from the center of mass falls inside the base of the object. If the line falls outside the base of the object, it will tip over due to gravity.

Any force that causes an object to follow a circular path is called a centripetal force. If we swing a string with some washers tied to the end around over our head, we find that we have to keep pulling inwards on the string. This is the centripetal force pulling the washers in a circle. With a car going around a curve, the centripetal force is the friction of the road on the tires. In circular motion, centripetal force is at right angles to the path of the object.

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Centripetal force is an inwards acting force. However, in circular motion there seems to be another force pushing outwards. If we are in a car that rounds a curve, we get thrown to the opposite side of the car. The outward force we feel is called centrifugal force. But guess what-there is no such thing as centrifugal force. The reason we were flung outwards when our car turned is because there was no force acting on us! Consider: You are in a car that stops suddenly. You fly forward. You say that the reason you flew forward is because of inertia, not because of some force acting on you. Now suppose you are in a car that turns left. You fly to the right because that is the direction you used to be going, and according to the law of inertia you will keep going that way until another force acts on you!

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Just as an object moving linearly has linear momentum, a rotating object ahas angular momentum. Angular momentum=rotational inertia times rotational velocity. (Angular momentum is a vector quantity, but we won't do any problems concerning the vector nature of angular momentum in this tutorial). For the case of an object that is small compared to it's axis' distance, we can say that angular momentum=mass times velocity times radius, or angular momentum=mvr.

Just as linear momentum is conserved, angular momentum is also conserved. That means that the product of rotational inertia and rotational velocity at any one time is the same as the product at any other time. Consider a man on a rotating turntable with a weight in either hand. As he holds his arms outstretched, he rotates. When he pulls his arms in, he decreases his rotational inertia, so to conserve angular momentum, his rotational speed must increase. So he rotates faster with his arms in than with his arms out.