00:01
Shown with the red color, this is the rod of length 2 meter and mass 9 kg.
00:09
At the end of the rod, we have a metal sphere of radius r equal to 0 .3 meter and mass of the sphere 8 kg is hanging.
00:20
This is a sort of pendulum, but it is different from a normal pendulum because in a normal pendulum, the string has no mass i mean the string is has no weight and is negligible mass right but here the string is replaced by a rod of length l so this is a rod not a string now this pendulum was hanging normally then a point mass shown by the green color here moving with a velocity vi here hits and mass 2 kiz hits the sphere at the end of the rod means it hits somewhere here.
01:08
And because of the initial kinetic energy of this point mass which is moving this way, the the complete pendulum, the rod and the sphere, they move, they shift somewhere here.
01:24
I'm showing it with a single line.
01:26
This is a rod, right? and now here we have a sphere like before and the point mass gets stuck to this rod at the end of the rod.
01:48
And the angle by which this system swings is theta equal to 25 degrees.
02:00
Now, first we need to find out the moment of inertia of the system.
02:07
Now this is a system of three particles.
02:12
The first particle is the sphere, second particle is the rod, and the third particle is this point mass.
02:20
We have to find their moment of inertia about this axis passing through the pivot point.
02:27
In fact, the axis is perpendicular to the point.
02:30
Surface of the whiteboard and passing through this point this is a hinge point or a p means pivot point right this is the axis so we know that the total moment of inertia of a system about having multiple particle about the same axis is is is nothing but the algebraic sum of moment of inertia of each particle of the system about the same axis.
03:06
So here the total moment of inertia of pendulum is equal to moment of inertia of sphere plus moment of inertia of rod...