00:01
Hello, in the question we have given that a solid disk of mass m, so this mass is given that is 0 .9 kg and radius of 0 .25 meters, so this r is given that is 0 .25 meters is suspended vertically and is free to rotate about its center without friction.
00:27
A point object has same mass as disk is placed at an angle of 20 degrees clockwise from the top along the rim causing the disk to rotate.
00:45
So, this theta is given to be 20 degrees, so the acceleration due to gravity is given, so we have to find out the angular speed omega f of the disk when the object is directly below the center of the disk.
01:08
So, when the this object is below the center of disk, so over here we have to see the system.
01:15
So, the system is we have this disk, we have this disk of radius capital r is given, sorry, we have this disk of radius capital r and over here we have this particle, so over here we have this particle and this particle makes this disk rotate.
01:55
So, over here, so let's say the particle is over here, now what happens is, so we have to find out the angular velocity when this particle comes over here right at below.
02:09
So, we will use the energy conservation but before that let us find out the moment of inertia of system.
02:17
So, moment of inertia of system is we will call it as i, so that is equals to the moment of inertia of the disk that is 1 by 2 mr square plus the moment of inertia of that particle that is mr square.
02:36
So, this will give us i as equals to 3 by 2 mr square.
02:42
Further, now we will use the energy conservation.
02:46
Now, initially when this object, when this particle comes over here, so its angular velocity, its kinetic energy is 0, so only the height will be responsible over here.
03:00
So, this will be the height which we will be considering right from the reference point.
03:08
So, this is the height.
03:11
Now, so we can write energy conservation.
03:15
So, we will apply the law of conservation of energy.
03:21
So, we will apply energy conservation.
03:24
So, that is initial energy is equal to the final energy...