Uniform Circular Motion

Nothing in this universe is absolutely stable. Everything changes position or orientation. This change is called motion. The common motions are translation and rotation. Both of them have the same velocity and acceleration.

The translation is the motion that we find in a line or a curve. Rotation is the motion that we observe when the orientation of the body changes.

There are several other types of motion. These include circular motion, periodic motion, oscillatory motion, rotatory motion, and rectilinear motion. The circular motion is when an object rotates along a circle or a circular path. Rotational motion is further classified into uniform and non-uniform.

Uniform circular motion definition

We define uniform circular motion as the movement that we observe when a body moves on a circular path. It moves at a constant speed. The direction of the object changes when it moves in a circle. In this type of motion, the velocity changes, but the speed remains constant.

In every scenario, the movement of the object in a circle is tangent. The direction of the motion of an object and the velocity vector are the same. It is because of this reason that the direction of the velocity vector to the circle is also tangent.

Features of uniform circular motion

When an object moves in a circular path, it experiences acceleration. When there is a change in velocity of the objects, it is either the speed or the direction. We can identify these objects as accelerating objects.

When an object experiences uniform circular motion, the speed remains constant. But it is speeding up because of the change in its direction. The acceleration takes place in an inward direction.

The net force is another important characteristic of an object. This object is experiencing uniform circular motion. When the net force acts upon an object, the direction of an object is towards the circle’s center. This scenario is referred to as centripetal force.

It is because of the centripetal force, an object does not continue moving in a straight line. It never deviates from its aligned direction. The direction of the inward net force is perpendicular to the velocity vector. It is because of this reason, the direction of the object changes. Also, it experiences inward acceleration.

In simple words, when an object moves in a circular path, it experiences some acceleration. It acts towards the circle’s centre. It makes the object move in the assigned circular path. This is known as Centripetal/Radial acceleration.

Apart from acceleration, there is a force that acts towards the centre. It is in a uniform circular motion of an object. This force is called centripetal force. In contrast to this, there is a centrifugal force which serves the purpose of balancing the centripetal force. Centrifugal force acts outside the circle.

Uniform circular motion formula

Considering, w = angular velocity, v = magnitude of the velocity, and r = radius of the given circle.

Radial or centripetal acceleration for uniform circular motion is: 

ar=v2/r=2r

Let us assume, m = mass of the particle. Considering the second law of motion,

F=ma

mv2/r=m2r

The above equation formulates the origin of centripetal force.

Angular displacement

It is the angle that forms between the position vector and the centre. Let us assume, dS = linear displacement and r= circle radius.

d=dS/r(Radians)

Angular velocity

It is the rate at which the angular displacement changes.

=d/dt(Radian/sec)

In the case of uniform circular motion, the formula for angular velocity 

= v / r

Angular acceleration

It is the rate at which the angular velocity changes. Let us assume = angular acceleration, d= difference in angular velocity, and dt= time difference. 

=d/dt(Radian/sec2)

It is always zero regarding uniform circular motion because of the angular velocity, which is always constant.

Magnitude of acceleration

a=v2 / r

Uniform circular motion examples

There are several examples that help to illustrate uniform circular motion. These include:

• A watch that has a second hand is always in motion on a circular dial.
• A nucleus is surrounded by its electrons. The electrons keep revolving and are in motion.
• A windmill has blades that are always in motion with the strokes of air.
• The artificial satellites are always in motion around the earth.
• Giant wheel
• A stone that is tied to a string
• Wall of death
• Merry-go-round
• Stirring a batter in a circular direction
• All the planets that are revolving around the Sun

Conclusion 

Anything that changes its position or orientation with time is called motion. There are several types of motion. In this article, we have discussed the uniform circular motion. It is defined as the movement that we observe when a body moves on a circular path at a constant speed.

We have also learned that when an object moves in a circular path, it experiences some acceleration, known as the centripetal acceleration. There is also a force involved which acts inwards and is known as centripetal force. Opposite to it is the centrifugal force.

Apart from these, we have discussed the formulas involved. Real-world examples are also included. Lastly, frequently asked questions are also included to help you prepare for any examination.