Uniform Circular Motion

The term ‘uniform circular motion’ refers to the movement of an object in a circle at a constant speed. In a circle, an object’s path is continually shifting. The object’s way is always tangent to the circle it is in. The velocity vector is tangent to the circle because the orientation of the object’s motion is the same as the orientation of the velocity vector. 

The net force exerted on an object as it rotates in a circular motion is the final motion characteristic. In this case, the net force exerted on the item is aimed at the centre. An inward force, or centripetal force, is used to describe the net force. An object would travel straight if it didn’t have this internal force. On the other hand, the item constantly changes direction and accelerates inward because the inward net force is directed perpendicular to the velocity vector.

Circular motion Angular speed and Linear speed 

• The angular velocity, denoted by the symbol omega (ω), refers to rotation per unit of time. Because it is a vector with a direction corresponding to either counterclockwise or clockwise motion.

• The amount of displacement per unit of time is measured by velocity v. It is a vector with a specific direction.

• The letter v is frequently used to represent the magnitude of the velocity and the speed (which is sometimes referred to as linear speed in these contexts to distinguish it from angular momentum).

• It is represented by the relationship v = rω, which means the relationship between the linear speed  v and the angular speed ω.

The Angular speed does not vary with the radius 

The angular speed (ω) does not change with the radius, although the linear speed v changes. So a point on the radius near the circumference of the circular path travels a more considerable distance per unit of time, moving faster than the point on the radius which is near the centre of the circular path. However, because every point on the line is going across the same angle simultaneously, the angular speed of every point on the line is the same.

Centripetal Acceleration 

Uniform circular motion is the most basic kind of circular motion, in which an object travels around a path at a constant rate of speed. Instead of being a constant, the linear velocity of an object travelling in a circle is constantly changing. The terms ‘acceleration’ and “velocity changes” are used interchangeably to describe changes in speed. In kinematics, an increase in velocity is defined as “acceleration.” Objects travelling in a uniform circular motion accelerate even though the magnitude of their velocity remains constant.

Every time you ride an automobile, you can feel this centripetal acceleration. Maintaining control of the steering wheel when driving in a turn is essential for achieving a smooth, circular motion. You feel like you’re being dragged out of your automobile seat as the curve becomes tighter. The observer’s imagination is the only thing that can keep the centrifugal force going. These effects are enhanced by steeper curves and faster speeds.

Acceleration is termed as a change in velocity in the direction of the change; in this case, the direction of the change is roughly toward the centre of rotation. (The centre of rotation is located in the middle of the circular path.) When we suppose that Δs is shrinking, the acceleration will point directly toward the centre of rotation. However, this is a complex condition to depict. Since centripetal means “centre seeking,” we refer to the acceleration of an object moving in a uniform circular motion as the centripetal acceleration.

Now that we’ve established that centripetal acceleration occurs in the direction of the centre of rotation, let’s talk about the magnitude of centripetal acceleration. The magnitude of centripetal acceleration for an item travelling at speed v in a circular route with radius r is given by the equation:

ac = v2/r 

ac can also be expressed in terms of the angular velocity magnitude, which is more convenient. As a result of substituting v = rω into the equation above, we obtain,

ac = (rω)2/r = rω2

The magnitude of centripetal acceleration can be expressed in terms of the magnitude of angular velocity, as follows:

ac = rω2

Conclusion

The term “uniform circular motion” refers to the movement of an object in a circle at a constant speed. In a circle, an object’s path is continually shifting. The object’s way is always tangent to the circle it is in. The angular velocity, denoted by the symbol ω, refers to rotation per unit of time. The amount of displacement per unit of time is measured by velocity v. It is a vector with a specific direction. The angular speed does not change as radius, although the linear speed v changes. In contrast to speed, the linear velocity of an object in circular motion is constantly changing because the object is continuously changing direction.