# What are the definitions of translational, rotational and rolling motion?

What are the exact definitions of pure translational , pure rotational and rolling motion? I am a class 11th student ... I find it difficult to exactly make a distinction between translational, rolling and rotational motions in my dynamics questions. So I want definitions that can fit in any situation.

## 3 Answers

Theese concepts usually arise in rigid body mechanics. So consider a rigid body which is a set of points in which the distance between any two points do not change. If this is too abstract you can just think of a piece of rock. One talks of translational motion when the body moves along a straight line, or more exactly when every point of the body travels on paralell lines. Easily put, it means sliding your rock on a table's surface. Rotational motion means that your body moves around a fixed axis, for exapmle consider the rotation of the Earth. Rolling is a special kind of motion, when a body is rotating around a moving axis. The axis is translating, while the body is rotating around it.

• suppose there is a rod rotating about an axis through one of its ends and perpendicular to the rod . By your definition it is rotational motion and we can apply rotational equations of motion but we can see that its centre of mass is also moving so we can also apply translational equations of motion . So is it a combination of both the motions ? – Varun Chandra Apr 10 '16 at 15:12
• @Varun Chandra In that case, the rod is rotating about its center of mass while the center of mass is revolving about the fixed end. So it is two rotations combined, which you can reduce to one rotational motion to make things easier. You cannot call it rolling since the center of mass is not translating. – thedude Apr 10 '16 at 15:18
• @thedude How can you say that centre of mass is not translating ? I have the frame fixed on the axis I specified . Accordingly the centre of mass is covering distances with the passage of time so it should be translating .... centre of mass is in circular motion so it should be translational also ....... – Varun Chandra Apr 10 '16 at 15:28
• ,, One talks of translational motion when the body moves along a straight line, or more exactly when every point of the body travels on paralell lines." So no, that is not translational movement at all. The center of mass is always moving during rotation, except when the rotational axis moves through it. – Tamasger Apr 10 '16 at 15:31

I haven't given the exact definitions, but instead given examples on what each of the three are. This will help you get your head around the topic, and be able to get more understanding when you encounter the problem again later.

Translation is when the centre of mass of a body moves from one point to another. An example is just pushing a book along a surface.

Rotation (without any translation) is just a body spinning in place, with its centre of mass fixed. An example would be a spinning top, or coin, spinning but staying in one place.

Rolling motion would be when a body is both rotating and moving. Imagine a ball rolling down a hill. It has rotational movement, but also is moving along a path.

I didn't use any equations to keep it simple, but feel free to ask if this isn't clear!

• Suppose a rod is rotationg with the axis at one of its end . Its centre of mass is moving and it is rotationg also so is it a rolling motion ? – Varun Chandra Apr 10 '16 at 15:01

The first (accepted answer) gives a good definition of translational and rotational motions. I have added this answer as I believe I can expand on Rolling motion a bit more. I know the OP asked for a definition of rolling but what I add here is more of an explanation since the physics of Rolling can be quite confusing. For a circular object (considering the wheel of a car for example) to roll (without slipping) there is translational velocity and rotational velocity.

Consider a wheel of a car moving to the right; At the top of the wheel the vectors corresponding to the translational and rotational velocities add together as the they are moving in the same direction as the wheel (or car) moves along to the right.

To understand this better; One must realize that the wheel rotates counter-clockwise, which must be true due to Newtons' third law of motion such that the ground (earth) will exert an equal but opposite force on the wheel in order to make it move forwards (to the right). So the earth is essentially rotating clockwise (negligible due to mass difference of course). But this means that the rotational velocity vector at the top of the wheel is to the right just as the translational velocity vector is also.

Whereas the bottom section of the wheel is rotating in the opposite direction to which the wheel is moving along (as the car moves); The vector corresponding to the rotational velocity is in the opposite direction to which the car moves. So these two vectors subtract and they subtract to give exactly zero. This must be the case as the point of contact of the wheel with the ground has a net velocity of zero. If this were not the case we would have skidding (or slipping).

If you drive a car you will understand this intuitively; Since if you were to brake suddenly the wheel would move (translate) forwards as there is no longer any rotation of the wheel as the brakes have been applied. So you would get skidding or (slipping).