 focus here let's take a v like this it's a v which is moving forward and velocity central mass is given as vcm vcm okay and let's say angular velocity is omega is this which points on the rigid body all the points every point have the same angular velocity on the rigid body okay so i don't need to specify which point has this angular velocity entire rigid body has omega so if one point is rotating for example you're observing with respect to center of mass and what angular velocity the other points will rotate with respect to center of mass same omega okay with respect to center of mass all the points rotate with omega only which is the angular velocity of the entire rigid body also with respect to center of mass is observing he himself is not rotating if suppose someone observer rotates and then observe but is observer in a straight line angular velocity will remain omega only if i get into too much of explanation it doesn't get simplified like you have to dig deeper and deeper it becomes more and more important okay so at times i'll tell you just to take it on the face right now tell me related to center of mass what is the velocity of this point and in which direction if the release is r is moving in a circle with respect to center and with respect to center of mass which direction so this is with respect to center of mass r omega that point at this point can you draw it with the direction of cube which side r omega dot omega things are simple okay so we keep it simple okay this is r omega that side and this is r omega okay now tell me stop talking a point over here this angle is 45 degree and the distance is r by 2 from the center what is the relative velocity of this point with respect to center r by 2 may not be the direction it will be 90 degree to this point is moving in a circle so it will be tangent to the circle which is like this if this is the radius it has to be perpendicular a tangent yes or no the velocity of this point related to the center of masses r by 2 omega like that it is a circular motion you have only found out center of mass so can you find the total velocity of these four points oh it it is in this direction the total velocity of this point is r omega minus vcm this way or vcm minus r omega that way so total velocity is just vcm square this 90 degree they affect this point r omega plus vcm this is as shown so total velocity will be again root over r omega square plus vcm square and if you do the vector addition that velocity will be this way vector chapter which is adding a little bit of diagonal views so isn't it much easier to observe first with respect to center of mass and then add whatever center of mass is doing to find that total velocity if you don't do that the motion of all this point become very complicated this point as this will move forward will follow some weird path it will do something weird let's solve this question simple one draw a circle as soon as this circle omega as shown and the center is going forward cm okay and this given that vcm is equal to r omega it is given you need to find the total velocity of this point which is at a distance of r by 2 and making an angle of 30 degrees down like this and how much will be this velocity for vcm by 2 so this is r by 2 into omega vcm on it this velocity I have to add this 90 this is how much 60 so this is 60 degrees so I have to add two vectors one vector is this other is that this is vcm and this is vcm by 2 and this angle is 60 degrees can you find out now total velocity will be vcm square plus vcm square by 4 plus 2 into vcm square by half of 60 so this is root over vcm square plus vcm square by 4 plus vcm square by 2 how much is this what vcm root 7 by 2 so it becomes very simple to first observe with a vector center of mass and then add what center of mass is doing so find the total velocity okay now let's see acceleration what it can do an object which is accelerating with angular acceleration alpha and linear acceleration k you find the acceleration of these four points quickly plus a you don't know minus a this is alpha r this is a here is alpha r and there is a okay tell me what is wrong some centripetal acceleration we are ignoring we are ignoring centripetal acceleration all of you understand this okay if something is moving in a circle there will be centripetal acceleration also fine for that i need to know the velocity but tangential acceleration at this point the centripetal acceleration will be towards the center like this so tangential will be a minus alpha r of this point what about tangential acceleration of this point how much will be alpha r tangential will be alpha r tangent is this direction radial is that direction tangential acceleration of that is alpha r radial will be a minus v square by r v square by r is towards the center everywhere towards the center this point tangential acceleration is alpha r tangential radial is v square by r this point tangential is alpha into r radial is a plus v square by r so these are the small small nuances you have to take care when you deal with the entire gene coding okay any doubts in now anything and all these whatever we are discussing it is not part of any textbook i'm just telling you how you can analyze if something comes like this as a problem okay any doubts