## How can an object spin at constant angular velocity when its parts are accelerating?

### How can a spinning object keep constant velocity with the direction of its parts changing at every instant?

When you consider an object as rotating, you normally stop thinking of its parts as moving in their own independent ways and treat the whole assembly as a single object. While it’s true that the various parts of that object are accelerating in response to internal forces those parts exert on another, the object as a whole is doing a simpler motion: it’s rotating about some axis. This ability to focus on a simple motion in the midst of countless complicated motions is an example of the beautiful simplifications that physics allows in some cases.

## When you push on a rotating object, when are you doing work?

### When you push on a rotating object, when are you doing work?

That’s an interesting question and requires two answers. First, if you push on a part of the rotating object and that part moves a distance in the direction of the force you exert, then you do work on it. In principle, it is possible to identify all the work that you do on the rotating object via this approach.

However, it is also possible to determine the work you do entirely in terms of physical quantities of rotation. If you exert a torque on the rotating object and it rotates the an angle in the direction of your torque, you again do work on the object. That’s the rotational version of the work formula: whereas force time distance is the translational work formula, torque times angle is the rotational work formula.

An important complication arises, however, in that you must measure the angle in the appropriate units: radians. The radian is the natural unit of angle and is effectively dimensionless (no units after it). When you multiple the torque times the angle in radians, the resulting units are those of work and energy. If you use a non-natural unit of angle, such as the degree, then you’ll have to deal with presence of the angle unit in your result.

## Rotating “up” or “down” — is that like clockwise and counter-clockwise?

### When an object is rotating, both the “up” and “down” directions point along the vertical axis. Do they correspond to clockwise and counterclockwise?

Yes. Distinguishing between the two opposite directions of rotation using words alone requires that everyone agree on what to call those two directions. It also requires that everyone have an artifact that they can use to identify which direction is which. When something is spinning about a vertical axis, a carousel or merry-go-round, for example, then physicists name the two possible directions of rotation “up” and “down” and use a right-hand rule to identify which is which. Since most people have a right hand and know which hand it is, the necessary artifact is built-in.

In more common language, the two directions might be called “clockwise as viewed from above” and counter-clockwise as viewed from above”. In this case, the artifact is an old-fashioned analog clock and is probably more of a remembered artifact than one that is in the room with you. Nonetheless, that common naming convention is fine; it’s just wordier than the physicist’s version.

## What is torque?

#### 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) du…

#### 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.

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

#### 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…

#### 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 mot…

#### 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 i…

#### 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?

#### 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.