Solved Examples on Dynamics Of Circular Motion
Example 1: Find the angular velocity of a body that is moving at a speed of 10 m/s in a circle of radius 2 m.
Solution:
Formula for angular velocity is given by,
ω = v/r
Given:
v = 10m/s and r = 2 m.
ω = v/r
ω = 10/2
ω = 5 rad/sec
Example 2: Find the force acting on a particle of mass 5 kg moving in a circle of radius 4 m at an angular speed of 20 rad/s.
Solution:
Formula for centripetal force is given by,
F = mrω2
Given:
ω = 20 rad/sec, r = 2 m and m = 2Kg
F = mrω2
F = 2×2×(20)2
F = 1600 N
Example 3: An insect moves in a circle of 4 m radius and completes 20 revolutions per second. Find the angular velocity, linear velocity, and acceleration.
Solution:
The body moves at 20 revolutions per second.
ω = Angle Cover per Second
= 20(2π)
= 40πAngular velocity is 40π rad/s
Linear velocity is given by,
v = rω
Given:
r = 4 m
v = (4)(40π)
v= 160π m/s
Acceleration will be given by,
a = v2 / r
a = (160π)2 / 4
a = 64000 π2 m/s2
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.