5 Momentum Conservation & Impulse Momentum Theorem | Centre of Mass Class 11 | JEE Main & Advanced

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Topics covered in this Chapter Centre of Mass Class 11 lecture by ABJ sir IITD with timestamp:

00:00 - 31:37 COM Problem 1: Based on the Momentum Conservation. In this problem, we have a smooth horizontal wire attached with two ends, and a bead of mass m is connected to a particle of mass 2m with a horizontal massless string. (According to the given diagram) This complete system is released. We have to analyze the motion of the bead and particle. This question is PYQ of Olympiad. In this problem, ABJ Sir uses the Concept of COM, the law of conservation of linear momentum, energy conservation, and many concepts. With the help of this problem, ABJ Sir Discusses every simple concept in this chapter.
1. Motion of the Bead and the particle (Analyse)
2. Motion of COM of this system - COM is moving only in the vertical direction.
3. Bead is performing oscillatory motion of amplitude (2L/3).
4. Particle of 2m mass is performing Circular motion about mass m (bead).
5. Maximum Speed of the Bead. (at the median) - Using Momentum Conservation and total mechanical energy conservation.
6. Tension in the string and normal force b/w wire and bead when string becomes vertical.

32:03 - 36:37 Impulse: Impulse in Physics is a term used to describe or quantify the effect of force acting over time to change the momentum of an object. It is represented by the symbol J and is usually expressed in Newton seconds or kg-m/s. It is a vector quantity.
Impulse is often stated to be the product of the average net force that acts on an object for a certain duration. The equation for impulse is given as, J = F⋅Δt . Area under the F-t Curve represents the Impulse.
36:40 - 40:52 Impulse Momentum Theorem: The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum. It proves that the change in momentum of an object depends not only on the amount of force applied but also on the duration of force applied.
41:22 - 45:51 COM Problem 2: Based on the Impulse Momentum Theorem. In this problem, we have an elastic ground, and a ball of 200 g is released from a height of 20 m. This ball will strike the ground, and the direction of its motion will change. We must find the ball's impulse when it strikes the ground.
46:05 - 57:50 COM Problem 3: Based on the Impulse Momentum Theorem. In this Problem, we have a ball of 400 g is strike the ground according to given diagram . We have to find the impulse the ground applies on the ball when it strikes the ground. Also find the friction coefficient b/w ball and surface. To solve this problem, ABJ Sir used Impulse Momentum Theorem.
58:43 - 01:03:58 Force by Raindrops/Hailstones on a surface: This topic can be explained using the Impulse momentum theorem. A change in the momentum of a raindrop will apply force on the surface; we can find the value of force using the impulse-momentum theorem.
01:03:58 - 01:08:15 COM Problem 4: Based on the Impulse Momentum Theorem. In this problem, we have a ground surface, and raindrops (each of mass 2 gm) are striking to the surface vertically with a velocity of 20 m/s and rebound with a velocity of 10 m/s vertically. The rate of striking raindrops to the surface is 10000 per sec. We have to find the force on the surface.
01:08:56 - 01:16:55 COM Problem 5: Based on the Impulse Momentum Theorem. In this problem, we have a hinge on a smooth horizontal surface (The situation is given according to the diagram). We have to find the speed of the particle just after the string got taut. Also, find the impulse of the tension when the string becomes taut.
01:17:11 - 01:28:40 COM Problem 6: Based on the Impulse Momentum Theorem. In this problem, we have a smooth horizontal surface, and a particle of 1 kg (The situation is given according to diagram). We have to find the velocity of particle just after string got taut. Also find impulse of the tension when string just become taut.