# Translational and rotational motion: the basic differences.

An object can come across two types of motion such as translational and rotational motion. These motions differ in the way that they make the object move through space. Translational motion is defined as the motion of an object in a straight line without any rotation. On the other hand, rotational motion is an object’s motion around an axis.

## Translational and rotational motion:

An object can come across two types of motion such as translational and rotational motion. These motions differ in the way that they make the object move through space. Translational motion is defined as the motion of an object in a straight line without any rotation. On the other hand, rotational motion is an object’s motion around an axis.

## Translational and rotational motion: length of the object matter.

One important and significant difference between translational and rotational motion is that motion affects the length of the object. When an object goes through translational motion, its length remains constant. As anybody observed when an object moves from one point to another in a straight line, the length of the object does not change, rather remains the same. However, during rotational motion, the length of the object can change. Because different parts of the object move at different distances from the axis of rotation.

For a better understanding of the above facts, consider an example of a rotational stick. When a stick is spun around its axis, the result is rotational motion. As the stick moves, different points of the stick rotate at different distances from the axis of rotation. The point which is at a farther distance has to cover the greatest distance to complete one rotation than the points that are closer to the axis.

This is the reason which causes the stick to deform and the length of the stick changes. The extent of deformation of the stick depends on the distribution of mass along the stick and the speed of rotation.

## Translational and rotational motion: where forces affect.

Another significant difference between translational and rotational motion is the way that forces affect the motion of the object. In the case of translational motion, forces cause the object to move in a straight line. The acceleration of the object is directly proportional to the force applied to the object in translational motion and the force is applied to the centre of the mass of the object. This implies that the object’s motion is solely determined by force applied to it.

On the other hand, in rotational motion, forces cause the object to rotate around an axis. The extent of rotation of the object is determined by the distribution of mass along the object and the axis of rotation. The distribution of mass affects the moment of inertia of the object. The moment of inertia is the force that resists any change in angular acceleration.  The greater the moment of inertia more amount of force is required to cause the object to accelerate.

The direction of the force also affects the motion of the object. If the force is applied perpendicular to the axis of rotation, that causes the object to move/accelerate rotationally. If the force is applied parallel to the axis of rotation that causes the object to accelerate transnational.

Similarly, the direction of the force affects the motion of the rotational body. The speed of the rotating object will increase if the force is applied in the direction of rotation and the speed will decrease if the force is applied against the direction of the rotation of the object.

## Translational and rotational motion: the energy transformation.

The translational and rotational motions also differ in how both motion transfer energy. In translational motion, the energy is transferred by the object moving from one point of place to another. Such energy transferred is proportional to the force applied to the object and the distance covered by the object. However, in rotational motion, the energy is transferred by the rotating object around the axis. The energy transfer is proportional to the object’s moment of inertia, the object’s speed, and the torque applied to the object.

## Translational and rotational motion: some examples.

Some common examples are given below for better appreciation in respect of both the motions,

### Translational motion: examples.

• A car is driving on the road.
• A train is running on the track.
• A person is walking from one place to another.
• A ball rolling down the hill.
• A boy is running on the road.

### Rotational motion: examples.

• A spinning top rotating around its axis.
• Earth orbiting the sun.
• A car tire rotates while the car is on moving.
• A dancer spinning on her one foot.
• A satellite moving around the planet in a fixed orbit.

## Translational and rotational motion: formulas.

The formulas for both motions are different as they represent different types of motion.

### The formula for translational motion.

The formula for the translational motion can be written as,

d=v*t

where,

d=distance travelled by the object, v=velocity of the object and t= time taken by the object to travel the said distance.

### The formula for the rotational motion.

The formula for the rotational motion is not as simple as translational motion, rather it depends on specific parameters of the object in motion. According to which specific formulas can be written as, such;

• Rotational speed, ω = θ/t where ω is the angular speed( in radian/second), θ is the angular distance covered by the object and t is the time taken to rotate through that angle.
• Tangential speed, v=r ω, where v is the tangential speed( in meter per second), r is the distance from the axis of rotation to the point on the object that is moving and ω is the angular speed( in radian/second).
•  Moment of inertia; I=∑mr2, where I, is the moment of inertia,(in kilograms per square meter), m is the mass of each particle in the object and r is the distance from the axis of rotation to each particle.

## Conclusion:

We conclude that the difference between translational and rotational motion has significant implications for the behaviour of the objects in motion. These differences affect the length of the object, the forces that affect the motion of the object in one or more ways, and the way the energy is transferred during motion. Understanding the above key parameters may give good feedback for understanding the physics of motion.