Inertia is a concept—the property of an object to resist any change in its velocity. Momentum is a vector quantity—the product of an object’s mass times its velocity and an important characteristic of a moving object. Momentum is important because it’s conserved and it’s conserved in large part because of inertia and related concepts.
Yes. If you spinning it about a vertical axis (so that gravity doesn’t exert a torque on it about its point), it will spin at a steady angular velocity almost indefinitely. Sliding friction does slow it gradually but if the point is very sharp, sliding friction there exerts very little torque on the top about its rotational axis. Because it’s unable to exert a torque on the ground, the top can’t exchange angular momentum with the earth. It spins on until it slowly gets rid of its angular momentum through sliding friction and air resistance.
When you exert a small horizontal force on the file cabinet, it doesn’t move because static friction between the ground and the file cabinet exerts a second horizontal force on the file cabinet that exactly balances your force. If you push the file cabinet west, the ground will exert a static frictional force on the file cabinet, pushing it east. The file cabinet will thus experience a net force of zero. You’ll have to push very, very hard before static friction will be unable to match your force. One you do exceed the limit of static friction, the friction will no longer be able to balance your force and the file cabinet will experience a net force in the horizontal direction. The file cabinet will then accelerate in the direction of your force.
A wagon starts its motion when you pull it or push it. If its wheels weren’t touching the ground, they would simply move along with the wagon and would not turn. However, they are touching the ground and the ground exerts a backward frictional force on them to keep them from sliding on the ground. This backward frictional force causes the wheels to begin turning.
A car starts its motion when the engine of the car exerts a torque on its wheels. These wheels begin to rotate. However, the wheels are again touching the ground and the ground exerts a frictional force on the wheels to keep them from skidding. This frictional force not only opposes the wheels’ angular acceleration, it also causes the wheels and the car to which those wheels are attached to accelerate horizontally.
I don’t think that it would be possible to detect any change in the earth’s rotation. The earth has a mass of about 6,000,000,000,000,000,000,000,000 kg, which is about 20,000,000,000,000 times the mass of all the people on earth. The earth’s moment of inertia is even more different than that of the people because much of the earth’s mass is located far from its rotational axis. So if all of the people gathered together and started spinning one way, the effect on the earth would be to make it spin the other way about 1/1,000,000,000,000,000,000 as much. The result might be that the day would change lengths by about a trillionth of a second. (1/1,000,000,000,000 s). That change is less than the natural fluctuations in the earth’s rotation rate, so no one would ever notice. You might find it interesting that the earth’s rotation rate changes slightly with the seasons because of snow in the mountains. When there is lots of snow in the northern hemisphere (during its winter), the earth’s moment of inertia increases just enough to slow its rotation. The day is a tiny bit longer than during our summer. People might be able to duplicate this effect by all climbing to the tops of mountains.
When you spin a merry-go-round, you exert a torque on it and it exerts a torque back on you. If you were free to rotate, this torque on you would be quite apparent. Suppose that the merry-go-round was located on an ice skating rink and that you were attached to the central pivot of the merry-go-round by a strap that went around your waist. As you spun the merry-go-round clockwise, you would begin to spin counter-clockwise. In fact, because your moment of inertia is much smaller than that of the merry-go-round, you would experience a much larger angular acceleration and would end up spinning much faster than merry-go-round. The reason that you don’t rotate like this after spinning a playground merry-go-round is that your feet touch the ground. As the merry-go-round exerts its torque back on you, you exert that same torque on the ground. The result is that the earth undergoes angular acceleration in the opposite direction from that of the merry-go-round. Because the earth’s moment of inertia is so huge, you can’t tell that it undergoes angular acceleration at all. It really does, just as the earth undergoes acceleration when you jump-you push down hard and the earth as it pushes up hard on you and you both accelerate away from one another. Since the earth is much more massive than you are, it doesn’t accelerate nearly as much as you do.
The lacrosse stick converts a big force into a small one. As you flip the stick, you do work on it—you push part of it forward while that part moves forward. You use a large force and the place on which you push moves forward a small distance. The stick, in turn, does work on the ball. It exerts a small force on the ball but moves that ball through a large distance. The products of force times distance are essentially equal (the stick itself takes some of the energy). The result is a very fast moving lacrosse ball that sails across the field.
The rule that’s used in the mechanics of rotation is always the right hand rule and that’s important. It represents a choice made long ago about how to describe an object’s rotation. Having made that choice, it says that the minute hand of a clock (which naturally rotates clockwise) points into the clock. You know that because if you curl the fingers of your right hand in the direction that the minute hand is turning, your extended thumb will point into the clock. There is no left hand rule because that was not the choice made long ago.
Angular speed is the measure of how quickly an object is turning. For example, an object that is spinning once each second has an angular speed of “1 rotation-per-second,” or equivalently “360 degrees-per-second.” Angular velocity is a combination of angular speed and the direction of the rotation. For example, a clock lying on its back and facing upward has a minute hand with an angular velocity of “1 rotation-per-hour in the downward direction.” The downward direction reflects the fact that the minute hand pivots about a vertical axis and that your right hand thumb would point downward if you were to curl your fingers in the direction of the minute hand’s rotation.
A balanced seesaw is simply one that isn’t experiencing any torque—the net torque on it is zero. Because there is no torque on it, it isn’t undergoing any angular acceleration and its angular velocity is constant. If it happens to be horizontal and motionless, then it will stay that way. But it could also be tilted or even rotating at a steady rate.