 # Uniform Circular Motion

When the motion of a body follows a circular path around a fixed point, it is known as circular motion. Here, uniform circular motion is a particular kind of circular motion where the motion of the body follows a circular path at a constant/uniform speed. The body has a fixed central position and so remains in equal distance from it at any known point.

When an object moves around in circular motion, there are many distinguishing factors to consider.

For Example: You have a ball attached to a string, and you move it uniformly over a circular motion; then, two interesting observations can be made.

1. The speed of the ball remains constant, tracing the circle over a fixed center point.

2. The ball remains in motion changing its direction constantly. As such, one can opt to stay on a circular path; the ball must change its direction in a constant manner.

We can gain an important observation from the 2nd point. According to Newton’s first law, there will be no acceleration without a net force. As such, there must be a force entangled with the circular motion. Nevertheless, for a circular motion to happen, the object must be acted by a net force, thereby resulting in the change of direction otherwise known as centripetal force.

Imagine that your friend has been kidnapped by aliens, and they have kept him in an object moving in circular motion. You will be able to save him, only after understanding the mechanism. This page will help you with the basics of circular motion.

From the above-mentioned theory, as long as your friend is in the field of circular motion, it will continue to follow the circular path. The moment the attachment breaks or you let go, the centripetal force stops acting, and your friend will be detached from the object. Then it will be easier for you to rescue your friend.

### Types of Circular Motion

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

1. Uniform circular motion or UCM,

2. Non-uniform circular motion

In the case of uniform circular motion, the angular speed & acceleration remains constant, whereas the velocity differs. However, in a non-uniform circular motion, both the angular speed and velocity changes.

### Uniform Circular Motion Formula

Consider a particle moving in a circle. It will have some acceleration acting at centre. This makes it move around the center position. As acceleration is perpendicular to the velocity, it only changes the direction of velocity, and the magnitude remains unchanged. This is the reason the motion is called uniform circular motion. This is otherwise called as centripetal acceleration, and the force that acts towards the center is known as centripetal force.

So, the centripetal force is the force acting on a body over a circular path. This point toward the centre of the body in motion.

Considering the uniform circular motion, the acceleration is:

ar = $v^{2}r$ = $ω^{2}r$

where,

a=acceleration, r=radius, v=velocity of the object, ω=angular speed

If the mass of the particle is m, from 2nd law of motion, you can find that:

F = ma

$Mv^{2}r$= $mω^{2}r$

So, if a particle moves in a uniform circular motion:

• Its speed is constant

• Velocity changes at every instant

• No tangential acceleration acts on the body

• Radial (centripetal) acceleration = $ω^{2}r$

• v=ωr

In the case of non-uniform circular motion, the tangential acceleration increases/decreases resulting in the acceleration to be the sum of tangential and radial acceleration.

1. What are Three Examples of Circular Motion.

Further, here are some circular motion examples with pictures:

a. An artificial satellite that rotates around the Earth at a constant height,

b. A car when it turns to a curve in a race track,

c. An electron that moves perpendicular to a uniform magnetic field

Now, the object’s velocity vector constantly changes in direction, and leads the moving object to be under acceleration by centripetal force. Also, without this acceleration, the object moves in a straight line as per Newton’s laws of motion.

Further, some common circular motion examples are:

• Athlete running in a circular path

• A stone tied to a string and rotated

• Merry-go-round

• Revolution of earth

• Spinning top

• Fan rotating

• Wheel of bicycle

2. Write any Four Examples of Uniform Circular Motion.

Following are the four uniform circular motion examples:

1. The motion of artificial satellites around the earth. Here, the gravitational force inside the earth makes the satellite stay in a circular orbit.

1. Tip of 2nd hand of a watch with circular dial

2. Motion of blades of the windmill

3. Motion of electrons around the nucleus

3. State the Important Properties of Uniform Circular Motion.

a. In a circular motion, there is a change in direction so that the body remains in acceleration.

b. Here the speed of the body remains in constant

c. The force which brings about uniform circular motion is the centripetal force which acts towards the centre

d. This is a periodic motion with definite frequency and period

e. The particle’s speed remains constant but velocity changes

f. It is an accelerated motion

g. Work done per periodic in uniform circular motion is zero.

4. What is the Difference Between Uniform Linear Motion & Circular Motion?

Uniform Linear Motion

1. An object is in uniform linear motion if it travels in a straight-line covering equal length in equal time-interval.

2. There is no change in direction

3. Here, the velocity and speed remains constant

4. Acceleration is zero.

Example: A car moving forward at a speed of 50km/h towards South direction.

Uniform Circular Motion

1. When a body moves in a circular path with a uniform speed

2. Here, the motion is in uniform acceleration

3. Speed remains constant, however the direction of motion changes

Example: An Athlete running in a circular path.

5. Give some Application of Uniform Circular Motion.

Some of real life and in everyday applications of uniform circular motion are:

1. Movements of minute hands of the clock.

2. Movement of blades of fan.

3. In most amusement parks , we see giant wheels, merry go round etc.

4. Revolution of planets around the sun.

5. Satellites orbiting earth or heavenly bodies.