Tag: seesaws

What is torque? — JPT, Calgary, Alberta

A torque is a physicist’s word for a twist or a spin. When you twist the top off a jar, you are exerting a torque on the jar and causing it to undergo an angular acceleration—it begins to rotate faster and faster in the direction of your torque. Similarly, when you spin a toy top, you do this by exerting a torque on the top and it again undergoes an angular acceleration.

We know that spinning objects on earth can lose their spin (angular momentum) due to friction (fluid or sliding) with the air or ground. However, if an object is set spinning in space, will it lose its initial angular momentum eventually or will it spin forever assuming no outside forces (e.g., gravity) act upon it? If it does come to rest, how does the earth maintain its spinning motion? — RD, Kingwood, TX

If a spinning object is truly free of outside torques—the influences that affect rotation—then it will spin forever. Angular momentum is a conserved quantity in our universe, meaning that it can’t be created or destroyed and can only be transferred between objects. Thus if you set an object spinning (by exerting a torque on it) and then leave it entirely alone, it will not be able to change its angular momentum. The earth is a good example of this situation—it’s almost free of torques and so it spins steadily about a fixed axis in space. Its angular momentum is essentially unchanging.

Since gravity acts at the center of rotation of a freely falling object (which is that object’s center of mass), gravity exerts no torque on freely falling objects. Because of that fact, even objects in orbit around the earth are essentially free of torques and satellites that are set spinning when they’re launched continue to spin steadily for centuries. The space shuttle astronauts encounter this result each time they release or catch a satellite. If they set it spinning when they let go of it, it will still be spinning when they retrieve it years later.

You said that when you were spinning around in circles, you were actually causing the earth to move, but it was too tiny a motion to notice. If everyone on the planet got together in one area and started spinning around at exactly the same time and with the same angular velocity, could the effect of the people causing the earth to move be noticed?

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.

Can you give me an example of when the angular acceleration is in a different direction from the torque applied?

When an object isn’t symmetric, it can rotate in very peculiar ways. If you throw a tennis racket into the air so that it is spinning about an axis that isn’t along the handle or at right angles to the handle, it will wobble in flight. Its axis of rotation will actually change with time as it wobbles. If you were to exert a torque on this wobbling tennis racket, its angular acceleration wouldn’t necessarily be along the direction of the torque.

Given a lever long enough, could you move the world?

Yes. Of course, you would need a fixed pivot about which to work and that might be hard to find. But you could do work on the world with your lever. If the arm you were dealing with was long enough, you could do that work with a small force exerted over a very, very long distance. The lever would then do this work on the world with a very, very large force exerted over a small distance.

How can cats turn their bodies around to land on their feet if they fall and how can people do tricks in the air when they are skydiving if you’re supposed to “keep doing what you’ve been doing” when you leave the ground?

Cats manage to twist themselves around by exerting torques within their own bodies. They aren’t rigid, so that one half of the cat can exert a torque on the other half and vice versa. Even though the overall cat doesn’t change its rotation, parts of the cat change their individual rotations and the cat manages to reorient itself. It goes from not rotating but upside down to not rotating but right side up. Overall, it never had any angular velocity. As for skydiving, that is mostly a matter of torques from the air. As you fall, the air pushes on you and can exert torques on you about your center of mass. The result is rotation.

Is moment of inertia determined only by mass, as inertia is in translational motion?

No, moment of inertia embodies both mass and its distribution about the axis of rotation. The more of the mass that is located far from the axis of rotation, the larger the moment of inertia. For example, a ball of dough is much easier to spin than a disk-shaped pizza, because the latter has its mass far from the axis of rotation.

Shouldn’t the seesaw be completely horizontal in order to be balanced? How can it be balanced if it’s not horizontal?

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.

What exactly are angular speed and angular velocity?

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.