Table of Contents

**Introduction: **

When an object moves in two coordinates such as x, y or y, z, and so on then the motion is there in a plane. The projectile motion is one of the examples where the object moves in both horizontal and vertical directions. The uniform circular motion is another example of the two-dimensional motion where the object moves with the uniform speed in a circular motion while the velocity keeps on changing at every point because the direction of the velocity vector keeps on changing.

Whenever an object travels in a circular motion at every point some of the acceleration is experienced by the object and this acceleration acts towards the center of the circle which makes that object move in that circle. This acceleration is called Radial acceleration or centripetal acceleration.

During a uniform circular motion, the force acting towards the center is known as the centripetal force and in order to balance that force, the force that acts outside the circle is called the centrifugal force.

The Centripetal force always keeps acting towards the center. The direction of the velocity always remains tangent to the circle at all points. The acceleration vector will always be perpendicular to the velocity vector and therefore it will always point towards the center. Mathematically the angular velocity is given as, w=v/r Where, w= angular velocity, v = magnitude of velocity, r = radius of the circle Mathematically the magnitude of the acceleration is given as a=v2/r The value of the angular acceleration is always zero in the uniform circular motion due to the angular velocity that always remains constant.

**A brief outline of the topic: **

The uniform circular motion can be defined as the motion of an object in a circle at some of the constant speed. When an object moves in a circular motion inside the circle it will constantly change its direction. At some point, the object may move tangentially to the circle. Because the direction of the velocity vector is the same as the direction of the motion of the object then the velocity vector is directed tangent to the circle as well.

The object moving in a circle is an accelerating object. The accelerating objects are the objects which change their velocity by either changing the speed or by changing the direction. When an object undergoes the uniform circular motion it moves with a constant speed. It will accelerate due to its change in direction. The direction of the acceleration always remains inwards.

**A brief note of important concepts and laws: **

The uniform circular motion is the two-dimensional motion in which the object keeps moving with a uniform speed in a fixed circular direction but because the direction of the object keeps on changing at each and every point thus the velocity also keeps on changing. The direction of every point is the direction towards the tangent.

The final motion characteristic for an object which undergoes the uniform circular motion is the net force. The net force acting upon this object is directed towards the center of the circle. Here the net force is said to be an inward or the centripetal force. Without such an inward force an object would continue in a straight line and will never deviate from its direction.

There are two types of circular motion that can act upon a body in motion:

- Uniform circular motion
- Non-uniform circular motion

In the uniform circular motion, the angular speed and the acceleration remain constant and the velocity differs. In the non-uniform circular motion both the angular speed and the velocity keep changing.

**Uniform circular motion **

Let us consider a particle moving in a circular motion. It will contain some acceleration acting at the center. This will make it move around the center position in a particle. As the acceleration is perpendicular to the velocity it will only change the direction of the velocity and the magnitude will remain unchanged. Hence, the motion is a uniform circular motion. This can also be called the centripetal acceleration and the force that acts towards the center is known as the centripetal force.

Therefore the centripetal force is the force acting on a body over a circular path.

Therefore, if a particle moves in a uniform circular motion then:

- The speed will be constant
- The velocity will change at every instant
- The tangential acceleration will not act on the body
- v=ωr

**Non-uniform circular motion**

If it is a non-uniform circular motion the tangential acceleration increases or decreases resulting in the acceleration to be the sum of the tangential and the radial acceleration.

Also read: **Law of Conservation of Linear Momentum**

**FAQs (Frequently Asked Questions):**

**Que: Give Practical examples of uniform circular motion. **

**Ans:** The practical examples of the Uniform Circular motion are as follows:

- The motion of the electrons present in an atom around the nucleus.
- In the wall of death, the bike has a normal force acting towards the center which makes it move in a circular motion.
- The Artificial satellite moving around the Earth is an example of the uniform circular motion. The gravitational force from the center of the earth exerted upon the satellite acts as the centripetal force for it.

**Que: A plane is flying with a speed of 120 m/sec; it makes a turn to join a circular path leveling with the ground. What will be the radius of the circular path formed if the centripetal acceleration is equal to the acceleration due to gravity?**

**Ans:**The centripetal acceleration is given as follows,

ac =v^{2 }/r

r= ac/ v^{2}

Let’s assume the acceleration due to gravity to be as 10m/sec2

r= 10 ×120× 120

r= 144000 m

radius= 144 km

Therefore the radius of the circular path formed if the centripetal acceleration is equal to the acceleration due to gravity is 144 km.

**Que: Name the device used for measuring the speed of rotation in electrical machines or in objects moving in uniform circular motors?**

**Ans: **The tachometer is the device that helps us to measure the speed of the rotation in electrical machines or in the objects moving in a uniform circular motion.

**Que: ****The property of conservation of energy is applied when an object moves in a uniform circular motion. How?**

**Ans: **The conservation of energy is a universal fact and this is properly applied when we move any object in the uniform circular motion when the object is moved by us in the uniform circular motion, the speed remains constant and therefore the kinetic energy also remains constant. Due to the constant change in the velocity, the momentum keeps on changing.