1 Definition of COM & COM of Different System | Centre of Mass Class 11 | JEE Mains & Advanced

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Topics covered in this Chapter Centre of Mass Class 11 lecture by ABJ sir IITD with timestamp:
00:00 - 01:30 Introduction of Chapter: Centre of Mass is important for JEE Mains & Advanced. The weightage of COM in JEE Advanced is high. Level of Chapter - Medium to Tough.
01:32 - 06:30 What is the Centre of Mass??: The Centre of mass of a body or system of a particle is defined as a point at which the whole of the mass of the body or all the masses of a system of a particle appear to be concentrated, and if an external force is applied, then it will have same translational motion as that the large body.
06:30 - 09:00 Mass Moment: Mass moment is multiplying the object's Mass and position vector. The unit of Mass Moment is kg-m. It is a Vector Quantity, and the direction of the mass moment is in the direction of the position vector.
09:10 - 12:48 Centre of Mass (COM) of a system of Discrete Particles: The Vector Addition of the weighted position vectors that point towards each object's Centre of Mass gives that system's Centre of Mass. The Centre of Mass is calculated separately for the components along each axis. To find the COM of a system of Discrete Particles, take the Ratio of Summation of mass moments and Summation of mass.
12:48 - 17:29 COM Problem 1: Based on the Centre of Mass (COM) of a system of Discrete Particles. In this example, there are three particles, and their position coordinates are given, and we have to find the COM of this system.
18:09 - 24:20 COM Problem 2: Prove that Summation of Mass Moments wrt COM is Zero. This is a very important point, and ABJ Sir proves this as an example, but we have to remember it as a property.
24:40 - 32:10 Centre of Mass (COM) of Two Point Masses: With the equations for the Centre of mass, let us find the Centre of mass of two point masses, m1 and m2, at positions x1 and x2, respectively, on the X-axis. The origin is taken arbitrarily so that the masses m1 and m2 are at positions x1 and x2 on the positive X-axis. The Centre of mass will also be on the positive X-axis. ABJ Sir Derived the Formula for given condition, it is an important Formula and we have to remember it. COM will lie nearer to heavier object and farther from lighter object.
32:17 - 37:55 COM Problem 3: Based on the Centre of Mass (COM) of Two Point Masses. In this example, there are two particles m1 and m2. If mass m1 is displaced by distance x1 as given. Then find displacement of mass m2 such that COM remains at same point.
37:58 - 42:46 COM Problem 4: Based on the Centre of Mass (COM) of Point Masses. In this example, there are four point masses in XY - Plane and there coordinates are given. We have to find the value of COM of this system.
43:32 - 46:21 Centre of Mass (COM) of the Continuous Body: The Centre of mass for asymmetrical objects having continuous mass distribution. If we consider an infinitesimal mass element dm such that upon integration within certain limits it will cover the whole body then the position vector of Centre of mass.
46:35 - 54:32 Centre of Mass of Uniform Rod: ABJ Sir derives the Formula of COM of the uniform rod of mass M and length L.
54:32 - 57:31 Important Point: In a symmetric system in which mass distribution is uniform, then COM lies at geometrical Centre.
57:52 - 01:06:08 COM Problem 5: Based on the Centre of Mass (COM) of Continuous Body. In this example, there is a Isosceles Triangle. Mass per unit length and length of each side is given and we have to find the Position of COM.
01:08:37 - 01:18:30 Centre of Mass of Uniform Half Ring: ABJ Sir derives the Formula of COM of the uniform half ring of mass M and Radius R.
01:18:34 - 01:24:10 Centre of Mass of Uniform Quarter Ring: ABJ Sir derives the Formula of COM of the uniform Quarter ring of mass M and Radius R.
01:24:40 - 01:30:33 Summary: COM of Different Rings. ABJ Sir summarize to find Centre of Mass of different types of Ring.