The study of circular motion is not only important in itself, but also an essential pre-condition for the study of rotational motion later under Mechanics. We start with the definitions of the **angular quantities in circular motion**.

Suppose a particle is moving in a circle in the counterclockwise direction. The centre of the circle coincides with the origin O of the coordinate system Oxy. The initial position of the particle is P_{1} at time t_{1}. The final position of the particle is P_{2} at a later time t_{2} . The **angular displacement** of the particle is equal to the angle swept by its position vector as it moves from OP_{1} to OP_{2} . Angular displacement is a pure number without dimensions. However, it is customary to express it in an artificial supplementary SI unit called **radian** (rad).

The **angular velocity** of the particle is its angular displacement per unit time. In **uniform circular motion**, the angular velocity has the same value at every instant. In **nonuniform circular motion**, the angular velocity keeps changing from one instant to another. The dimension of angular velocity is [T^{-1}] ; its unit is radian per second (rad/s) or simply per second ( /s) since radian is a dimensionless unit. The time taken by a particle to complete one revolution is known as its **time period**. The number of revolutions completed by the particle per second is called its **frequency**.

In the case of nonuniform circular motion, the **angular acceleration** of a particle is the rate of change in angular velocity with time.The dimension of angular acceleration is [T^{-2}] ; its unit is radian per second square (rad /s^{2}), or just per second square ( /s^{2}).

It is useful to note the **relations between linear and angular quantities**. A particle, moving in a circle of radius r, changes its position from P_{1} at time t_{1} to P_{2} at time t_{2} . The distance travelled by the particle is the length of the arc P_{1}P_{2} . This distance is equal to the product of its angular displacement and radius of the circle. Similarly, the linear speed of a particle moving in a circle at any instant is the product of its angular speed and circle's radius.

The linear acceleration of a particle in circular motion has two components: tangential and radial. The **tangential acceleration** at any instant is the product of its angular acceleration and circle's radius. The **radial acceleration**, or **centripetal acceleration** as it is more commonly called, is the product of angular speed squared and circle radius.

Circular motion of a particle with constant angular acceleration is analogous to motion in a straight line with constant linear acceleration. Therefore, it is possible to develop a set of **kinematic equations of circular motion** in the same way as we did it for rectilinear motion. These equations involve quantities such as angular displacement, initial and final angular velocities, and angular acceleration.

When a particle performs **uniform circular motion**, its angular acceleration is zero, which means its tangential acceleration is also zero. The only acceleration present is the **centripetal acceleration** directed radially towards the centre of the circle. According to Newton's second law, the particle experiences a net external force – directed radially inwards – of magnitude given by the product of the mass of the particle and its centripetal acceleration. This force is known as **centripetal force**. An example of centripetal force is the gravitational force exerted by the sun on the earth which makes the latter revolve round the sun. In a rotating non-inertial frame of reference, a particle experiences a pseudo force directed radially outwards. This pseudo force is known as **centrifugal force**.

When a particle performs **nonuniform circular motion**, its tangential acceleration and centripetal acceleration are both non-zero quantities. Therefore, by Newton's second law, the net external force acting on the particle is the resultant of a **tangential force** and a **centripetal force**. A sphere moving in a vertical circle at the end of a light string constitutes a case of nonuniform circular motion.

Angular Quantities In Circular Motion
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Derivation Of Centripetal Acceleration
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Two Accelerations Of Nonuniform Circular Motion
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Relations Between Linear And Angular Quantities
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Circular Motion With Constant Angular Acceleration
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Problems On Circular Motion With Constant Angular Acceleration
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Examples Of Uniform Circular Motion
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Examples Of Uniform Circular Motion II
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Examples Of Nonuniform Circular Motion
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Problems On Circular Motion I
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Problems On Circular Motion II
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Problems On Circular Motion III
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Advanced-Level Problems On Circular Motion I 1:03:41

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Advanced-Level Problems On Circular Motion II 1:11:15

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Advanced-Level Problems On Circular Motion III 1:18:10

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Advanced-Level Problems On Circular Motion IV 1:17:02

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Advanced-Level Problems On Circular Motion V 1:10:37

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Advanced-Level Problems On Circular Motion VI 1:13:31

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