A Comparison of Linear and Rotational Motions

Motion is the first phenomenon that humankind observed. From humans walking to the earth’s rotation, there are thousands of everyday examples of motion. However, motion can be classified into two major types, linear and rotational motion.

The distinction between these types of motion is the type of displacement that occurs. While linear motion deals with the movement of bodies in a given plane, rotational motion deals with the movement of bodies around a given axis. Let us look further in detail at the different types of motion.

Rotational Motion

Rotation is the movement in a circle of a body about an axis of rotation. Any 3d body object may have an indefinite number of rotation axes. When the rotation axis goes via the centre of the body’s mass, the body can be stated to be auto-rotating or spinning, and the surface cross-section of the axis is called a pole. A rotation about a totally external axis is called revolving or orbiting, usually when it is under the influence of gravitational force, then ends of the axis of rotation can be stated as orbital poles.

Rotational motion is due to the effect of the moment of force. When force is applied on one end of a body, and the force is such that the body has angular displacement, we call it rotational motion. This rotational motion causes a body to move around a given axis called the axis of rotation.

Linear Motion

It is very unlikely that uniform linear motion exists in day to day life. One example of linear motion is Newton’s first law of motion. The law states that when an object is in motion with no external forces acting on it with constant velocity, then the object will continue to stay in motion, but, in reality, motion on earth has many forces like friction and gravity are acting on the object in motion hence making it a non-uniform motion if we were to roll a ball in space that has no friction or gravity then said Newton’s law of motion is accurate also giving us uniform linear motion.

In non-uniform linear motion, we must also consider direction as a factor. The main difference between linear motion and non-uniform linear motion is that one is scalar, and the other is a vector quantity alongside small differences like constant velocity, zero acceleration, etc.

The motion is always depicted using vectors and graphs represented by the x and time component graph; if we were to plot a uniform linear motion graph, the plot would show a straight line across the graph as there will be no change in direction or speed.

To calculate the speed of any object, we use the formula

Distance = speed / time

Or d = s/t

Speed is scalar.

Difference between Linear Motion and Rotational Motion

Linear motion

1. The motion of an object along a straight line is known as linear motion.

For example, the motion of children cycling, cars running on the road, etc.

2. The distance travelled by an object is always measured as a straight line.

3. If the starting and ending point of the motion is along the same straight path, the magnitude of distance is equal to that of distance.

4. The rate of change of displacement is known as linear velocity, given by v = dx/dt and its SI unit is m/s

5. The acceleration of an object in motion is the rate of change in velocity. The formula for the acceleration can be written as

a = dv/dt

6. The inertia in linear motion is contributed by the mass and velocity of the object.

7. The equations for motion to study displacement, velocity, and acceleration are given as:

• First equation of motion, v = u + at

• Second equation of motion, s = ut + 1/2 at²

• Third equation of motion, v² = u² + 2as

8. According to Newton’s second law of motion, the force responsible for producing linear motion is given as F=mass x acceleration.

Rotational Motion

1. The motion of an object around a fixed point or object is known as rotational motion. For example, the motion of children in a merry-go-round, the motion of blades of a fan, etc.

2. The distance travelled by an object is always measured in terms of the angle described by an object with the centre.

3. The parameters like displacement, velocity and acceleration are changed as angular displacement, angular velocity and angular acceleration.

4. The rate of change of angular displacement is known as angular velocity. Denoted by omega (ω), given by

ω = dΘ/dt

SI unit is rad/s

5. The angular acceleration of an object in motion is the rate of change of angular velocity. Denoted by alpha (α), the formula for the acceleration can be written as

α=dω /dt

SI unit is rad/s.

6. The inertia in linear motion is contributed by the mass and square of the distance of particles from the axis of rotation. Here, it is termed a moment of inertia.

7. The equations for motion to study angular displacement, angular velocity and angular acceleration are given as

• First equation of motion, ω =ω₀+αt

• Second equation of motion, Θ=ω₀t+1/2αt²

• Third equation of motion, ω²=ω₀²+2αΘ

Where ω₀ = initial angular velocity, ω = final angular velocity

8. To produce rotational motion, torque is responsible, which is given by

Torque = moment of inertia and angular acceleration.

Conclusion

Motion is a fundamental observation in the physical world. All types of motion can be classified into three basic types: linear and rotational motion. In linear motion, the body is covering distance but without frequent changes in its direction. The force is acting on the body in the direction of the motion.

In rotational motion, all the particles in a body are moving in a circular motion around a given axis. The body is in rotational motion due to the torque or the moment of the force acting on the body.