## Unit – II A |

## Concept of Uniform Circular Motion:

### Uniform Circular Motion:

- The motion of a particle along the circumference of a circle with a constant speed is called uniform circular motion (U.C.M.).
- e.g. The motion of the earth around the sun. The motion of an electron around the nucleus.
- For uniform circular motion, the angular velocity (ω) is constant and its angular acceleration (α) is zero. Its tangential acceleration (a
_{T}) is zero. The centripetal acceleration (a_{C}) is constant. - Uniform motion is that motion in which both the magnitude and direction of velocity remain constant. In UCM the magnitude of velocity is constant but its direction changes continuously. Hence UCM is not uniform motion.
- In uniform circular motion, the magnitude of the instantaneous velocity remains the same but its direction changes continuously.

### Non-Uniform Circular Motion:

- The motion of a particle along the circumference of a circle with variable speed is called uniform circular motion (U.C.M.).
- e.g. When we switch on the fan then the tip of the blade of the fan starts from rest and ultimately acquires constant speed. The motion of the tip of the blade of the fan between these two incidents is non-uniform circular motion
- In a non-uniform circular motion, the magnitude and direction of the velocity change continuously.
- For non-uniform circular motion,

- In this type of motion, the angular velocity (w) changes continuously and there is angular acceleration (a) of the body. The centripetal acceleration changes continuously.

### Period of UCM:

- The time taken by a particle performing uniform circular motion to complete one revolution is called as a period of revolution or periodic time or simply period.
- It is denoted by ‘T’. The S. I. Unit of a period is second (s). Its dimensions are [M
^{0}L^{0}T^{1}]. - Let us consider particle performing uniform circulation motion. Let ‘T’ be its period of revolution. During the periodic time (T), the particle covers a distance equal to the circumference 2πr of the circle with linear velocity v.

### Frequency of UCM:

- The number of revolutions by the particle performing uniform circular motion in unit time is called as frequency (n) of revolution.
- The frequency is denoted by a letter (n) or (f). The S. I. Unit of frequency is hertz (Hz). Its dimensions are [ [M
^{0}L^{0}T^{-1}]. - In time T the particles complete one revolution. Thus the particle completes 1/T revolutions in unit time.

### Centripetal Acceleration:

- The acceleration of the body performing circular motion which is directed towards the centre of circular path along the radius is called as radial acceleration or centripetal acceleration.

### Centripetal Force:

- A centripetal force acting on a particle performing a circular motion, which is acting along the radius of a circle and directed towards the centre of the circle.
**Example:**

When a stone tied to one end of a string is whirled horizontally, there is an inward force exerted by the string on the stone called tension. This force provides necessary centripetal force for circular motion.

### Centrifugal Force:

- The imaginary force which acts on the particle performing a circular motion in the direction away from the centre along the radius of the circular path having the same magnitude as that of centripetal force is called as centrifugal force.
**Example:**

When moving car along a horizontal curved road takes a turn, persons in the car experience a force in the outward direction. This force is centrifugal force.