Uniform Circular Motion: Definition, Formula & Examples

Uniform Circular Motion is a motion where the acceleration and angular speed of a particle moving in a circle remains constant. Circular motion is described as the movement of an object in a circular path while spinning. It can further be divided into two types: uniform and non-uniform circular motion. 

• When the position of a body constantly varies with reference to a stationary object, the object is said to be in motion.
• All moving bodies change their position over time. 
• Uniform Circular Motion is when a body moves in a circular path at a constant speed.
• Due to the continual change in the direction of motion, the velocity of a body travelling at a constant speed in a circle is not uniform.

Key Terms: Uniform Circular Motion, Speed, Circular Path, Velocity, Acceleration, Centripetal Force 

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What is Uniform Circular Motion?

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The motion of a body going at a constant speed along a circular path is known as uniform circular motion. The velocity varies while the speed of the body in uniform circular motion remains constant.

• If a particle is travelling in a circle, it must be experiencing some acceleration, causing it to rotate around the centre.
• As this acceleration is always perpendicular to a particle's velocity, it only alters the direction of velocity rather than the magnitude, which is why the motion is circular and uniform. 
• The force acting towards the centre is termed centripetal force, and the acceleration is called centripetal acceleration (or radial acceleration).
• The moving object is accelerated by a centripetal force in the direction of the centre of rotation because the object's velocity vector is in a continually changing direction.
• According to Newton's laws of motion, the object would move in a straight line without this acceleration.
• When a rigid body rotates around a fixed axis that is not negligibly small compared to the path's radius, each of the body's particles describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varied with the axis' location.

Uniform Circular Motion

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Uniform Circular Motion Formula

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If the circular path's radius is R and the magnitude of the object's velocity is V. The object's radial acceleration will then be:

a_rad= \(\frac{v^2}{R}\)

This radial acceleration, once again, will always be perpendicular to the velocity direction. The SI unit for it is m²s^-2.

• The radial acceleration can alternatively be calculated using the motion's period, i.e. T. 
• T is taken as the length of time it takes to complete a rotation. It is measured in seconds.
• The velocity of an item traveling in uniform circular motion is equal to the circumference C of the circle divided by the period of time if the magnitude of the velocity is v. Thus,

\(V = \frac{C}{T}\)

• The circumference of the circle can be calculated as the radius R multiplied by pi.
• As a result, C = 2ΠR
• As a result, the velocity will be constant throughout the motion.

\(V = \frac{2{\pi}R}{T}\)

• Using this value in the radial acceleration equation, we get,

a_rad =\(\frac{4 \Pi^2 R}{T^2}\)

Also Read: Motion in a Straight Line

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Characteristics of Uniform Circular Motion

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In the case of uniform circular motion, the acceleration is:

ar = v²r = ω²r

If m is the mass of the particle,

F = ma

mv²r = mω²r

If a particle is travelling in a uniform circular motion, then:

1. It moves at a constant speed.
2. Velocity is constantly changing at each constant, v = R.
3. No tangential acceleration is present.
4. Its centripetal acceleration (radial) is ω²R.
5. v = ωr

There is some tangential acceleration in a non-uniform circular motion, which causes the particle's speed to increase or decrease. The resulting acceleration is referred to as the vector sum of the tangential and radial accelerations.

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Examples of Uniform Circular Motion

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The examples of uniform circular motion are as follows – 

• The motion of artificial satellites around the planet exemplifies uniform circular motion, which is kept in a circular orbit around the planet by the gravitational attraction of the earth.
• The moon revolves around Earth in a circular motion.
• The movement of electrons around the nucleus of an atom is a uniform circular motion.
• The rotation of the windmill blades.
• A watch with a circular dial has a uniform circular motion at the tip of the second hand.

Uniform circular motion, therefore, occurs when a body moves in a circular path at a consistent speed.

Uniform Circular Motion of a satellite around a planet

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Things to Remember

• A circular motion is defined as a body movement that follows a circular route. 
• The motion of a body going at a constant speed along a circular path is known as uniform circular motion.
• When a body moves in a circle at a constant speed, the work it does is zero. This implies that the centripetal force does no work.
• The moving object is accelerated by a centripetal force in the direction of the centre of rotation because the object's velocity vector is in a continually changing direction. 
• The frictional force between the tires and the ground provides the essential centripetal force for turning cars on the roads.
• The motion of artificial satellites around the planet exemplifies uniform circular motion.

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