Dynamics of Circular Motion
In this motion, the body is moving at a constant speed. Let’s say the radius of the circular trajectory on which the body is moving is “r”, and the speed of the body is v m/s. The figure shows the body going from point A to point B in time “t”. The length of the arc from point A to point B is denoted by “s”. In this, the angle covered by the object is given by,
θ = s / r
The image given below tells us about the Dynamics of Circular Motion,
The angular velocity of the body is defined as the rate of change of angle. It’s similar to velocity in the case of straight-line motion. It is denoted by the Greek symbol ω.
ω = dθ / dt
Using the relation given above for the angle covered.
ω = d / dt (s/r)
ω = ds / dt (1/r)
where,
s is the length of the arc (distance covered by the body)
v = ds / dt
where,
v is the speed of the body
Substituting the value in the equation,
ω = ds / dt (1/r)
ω = v (1/r)
v = rω
(or)
ω = v /r
The image given below shows the formula for angular velocity.
Dynamics of Circular Motion
Circular motion is a motion in which an object moves around a fixed point in a circular motion. It can be both uniform and non-uniform. If there is no tangential component of acceleration then it is a uniform circular motion, and if the tangential component of acceleration is present, then it is a non-uniform circular motion.
There are lots of examples around us in our daily lives where bodies perform circular motions every day. From the hands of the clock to a car turning on a banked road. All these are examples of circular motion. This motion can be classified into two categories – uniform circular motion and non-uniform circular motion. It is essential to know the dynamics and the equation of the body performing the circular motion. These dynamics allow us to analyze these motions and calculate the statistics related to the behaviour of the body in such motion.