Terms Related to Circular Motion
Object performing Circular Motion, there are several terms related to it which needed to be defined, such as angular displacement, angular velocity, angular acceleration, centripetal, and centrifugal force, etc. These terms are explained in detail as follows:
Angular Displacement
In the circular path, angular displacement is the difference of angle subtended by the position vector to the center from the initial to the final state. The unit of the angular displacement is Radians. The formula for angular displacement is,
dθ = dS/r
θ = S/r
Where,
- dS or S is the Linear displacement, and
- r is the radius of the circle.
Note: This formula (θ= S/r) is also the relation between linear and angular displacement.
Angular Velocity
Angular velocity is defined just like linear velocity, that is, Angular velocity is the rate of change of angular displacement. The unit for angular velocity is Radian/sec. It is given by the formula:
ω = dθ/dt
ω = θ/t
Where,
- dθ or θ, is the angular displacement of the particle, and
- dt or t is the time taken for the angular displacement.
Angular Acceleration
The angular acceleration is defined as the rate of change of angular velocity (w), The unit for angular acceleration is given as Radian/sec2. The linear acceleration is related to angular acceleration as, al = αr
The angular acceleration is given as,
α = dw/dt
OR
a=v2/r
Where,
- α is angular acceleration, and
- dw/dt is the rate change of the angular velocity,
Note: The value of angular acceleration is always zero in uniform circular motion since the angular velocity is constant.
Uniform Circular Motion
Uniform Circular Motion as the name suggests, is the motion of a moving object with constant speed in a circular path. As we know, motion in a plane only has two coordinates, either x, and y, y and z, or z and x. Except for Projectile motion, circular motion is also an example of motion in a 2-D plane.
In a uniform circular motion, the object moves with constant speed but not with constant velocity as the direction of the motion is due to the circular path always changing. From the motion of electrons in Bohr’s Atomic model to the motion of the hands of an analog clock, we can see Uniform Circular Motion around us.
In this article, we will learn about the details of Uniform Circular Motion i.e., formulas related to uniform circular motion, examples, and the equation of motion of the uniform circular motion.