Combined Translational and Rotational Motion - JEE Important Topic

Rolling motion is one of the most common movements seen in daily life. All wheels used in transportation, such as cars, buses, trains, aeroplanes, bikes, buffalo carts, and many other things with wheels attached to them, such as trollies, have a rolling motion. Let's start with a disc for clarity, but the result applies to any rolling body, rolling on a level surface. When the disc rolls, it is assumed that it is not slipping. This implies that the bottom of the disc in contact with the flat surface is always at rest on the surface. 

Now, there are two types of rolling motion: pure rolling and combined rolling. Pure rolling occurs when there is no slipping between the object and the surface. Combined rolling occurs when there is slipping between the object and the surface. In this article, let's study more about rolling motion, translatory motion definition and examples and many other concepts.

Understanding Rolling Motion

Rolling motion contains two types of motion: translational and rotational motion. It can also be said that rolling motion is a combination of translational and rotational motion. A body's translational motion is the movement of its centre of mass.

During a body's rolling motion, the surfaces that come into contact, deform slightly and this deformation is temporary; that is, when the areas of both bodies come into contact with each other, the body deforms temporarily. This phenomenon has a frictional impact effect, which is the component of the contact force parallel to the surface that resists motion.

What is Translation Motion ?

Translational motion, or translation motion, is the movement of an object from one point to another. The object can be moved in any direction, but it must move in a straight line. Translation motion can be represented using a vector. Rectilinear and curvilinear are the two types of translational motion.

• Rectilinear motion: When a body in translatory motion moves in a straight line, the type of motion is known as rectilinear motion. For instance, a car moving on the straight road, or a train running on a straight track.

• Curvilinear motion: It describes the movement of a body in translatory motion along a curved path. For instance, turning a car.

Examples of Translational Motion

• The movement of an object from one point to another without changing its orientation or shape.

• A type of motion in which an object moves along a path from one point to another.

• An example of translation motion is when a person walks across a room.

What is Rotational Motion?

Rotational motion is a type of motion in which an object or body rotates around a fixed point. The fixed point may be the centre of mass of the object, or any other point in space. The object may be rotating about its own axis, or it may be orbiting another object (such as a planet orbiting the sun).

Examples of Rotational Motion

• A merry-go-round at a playground

• A Ferris wheel

• A top

• The blades of a fan or propeller

Let us assume the velocity of the wheel’s centre of mass is vcm, which is its translational velocity. Since the rolling wheel’s centre of mass is at its geometric centre C, vcm is the velocity of C. It is parallel to the flat surface. If you observe, the wheel rotates along its symmetrical axis that passes through the centre of C. Thus, the velocity of each point on the disc, such as P0 ,P1 ,or P2 is made up of two parts i.e, the linear velocity vr due to rotation and the translational velocity vcm.

A Wheel Representing Certain Mass and Velocity

• Here, the magnitude of vr is ${{v}_{r}}={{\omega }_{r}}$, where r is the distance between the point and the axis and $\omega $ is the angular velocity of the wheel rotation about the axis. With regard to C, the velocity ${{v}_{r}}$ is perpendicular to the radius vector of the given point w.r.t C. ${{v}_{r}}$ is perpendicular to $C~P{}_{2}$ in this case.

• It’s simple to demonstrate that ${{v}_{2}}$ is perpendicular to the line ${{P}_{0}}{{P}_{2}}$. As a result, the instantaneous axis of rotation is defined as a line passing through \[{{P}_{0}}\]and parallel to $\omega $.

• Due to rotation, the linear velocity ${{v}_{r}}$, is exactly opposite the translational velocity, ${{v}_{cm}}$, at point ${{P}_{0}}$. Furthermore, the magnitude of ${{v}_{r}}$, in this case, is ${{R}_{\omega }}$, where R is the wheel’s radius.

• The condition that ${{P}_{0}}$ is instantaneously at rest requires ${{v}_{cm}}={{R}_{\omega }}$. Thus, for the wheel, the condition for rolling without slipping is ${{v}_{cm}}={{R}_{\omega }}$.

• This also means that the velocity of point ${{P}_{1}}$ at the top of the wheel ${{v}_{1}}$is ${{v}_{cm}}+R$or $2{{v}_{cm}}$ and is parallel to the level surface.

Difference Between Translational and Rotational Motion

Summary

We can summarise the whole article in a few important points. Rolling motion is a  combination of translational and rotational motion. Translational motion is the movement of an object from one point to another, whereas rotational motion is a type of motion in which an object or body rotates around a fixed point. When an object is moving in such a way that it combines two motions, it is called combined motion. When it comes to combination motion examples, it can be observed that the movement of wheels on a cycle combines rectilinear and rotatory motion. The fixed point may be the centre of mass of the object, or any other point in space. We have also seen the examples of these two motions. We hope you found the article useful!