CBSE Class 11th System Of Particles And Rotational Motion
System Of Particles And Rotational Motion
The chapter on rotational motion and the system of particles in the class 11 physics syllabus is crucial. It is frequently thought of as one of the most difficult topics in class eleven because it involves intricate theories, derivations, and formulas. It's critical to comprehend the nuances of this chapter given its significance in academic and competitive exams. Now, let's launch the blog and go over some key points regarding the rotation motion and particle system.
1. Definition of Rigid Body:
A rigid body is an idealization of a body that does not deform or change shape. Formally, it is defined as a collection of particles with the property that the distance between particles remains unchanged during the course of the motions of the body. Like the approximation of a rigid body as a particle, this is never strictly true. All bodies deform as they move. However, the approximation remains acceptable as long as the deformations are negligible relative to the overall motion of the body.
2. What is a center of mass?
The location where the entire mass of the framework is intended to be concentrated for translational movement is known as the Center of Mass. In a two-molecule framework, the
center of mass always sits somewhere in the middle of the particles and on the line connecting the two particles.
3. Motion of the Center of Mass?
An arrangement of particles' centers of mass moves as if all of the framework's mass were concentrated there and all external forces were applied at that location. The focal point of mass will have constant energy at that point, assuming no external cause continues to affect the body. Because of its constant speed and zero acceleration, MVcm = consistent.
4. Vector Products Of Two Products
Written as a × b, this vector represents the cross product of two vectors, a and b. Such a vector has a magnitude of ab sin, and the right-hand rule approach can be used to determine its direction.
5. Mechanical Equilibrium Cases in Rigid Body
Two scenarios, as discussed in the chapter on the system of particles and rotational motion, can be used to calculate the mechanical equilibrium of a rigid body.
When there is no translational equilibrium
If the rotational equilibrium is zero, then the total external torque is also zero. Torque is defined as a moment of force that is obtained by multiplying the force acting on the particle by its magnitude and the force's perpendicular distance from the particle's axis of rotation.
6. Moment of Inertia
The rotational inertia of a rigid body is called its moment of inertia. The moment of inertia of a rigid body about a particular axis can be computed as the product of the masses of the constituent particles and the square of each particle's perpendicular distance from the axis.
7. Theorems of System of Particles and Rotational Motion
The System of Particles and Rotational Motion consists of two important theorems that are necessary to understand in order to have a strong grip on this topic. The given theorems are:
A. The Theorem of Perpendicular Axis
His theorem states that the body's moment of inertia (I) for a particular perpendicular axis is always equal to the sum of the body's moments of inertia for two axes that are always at a 90° angle to one another in the body's plane and meet at the place where the perpendicular axis passes.
I = Ix + Iy
B. The Theorem of Parallel Axis
The moment of inertia I of a body about any given axis is always equal to its moment of inertia about a given parallel axis, according to the Parallel Axis Theorem, via the idea of the center of mass Icm.
I = Icm+ Ma^2
8. Angular Momentum and Law of Conservation Angular Momentum
Angular momentum is the next crucial subject in our notes on the particle system and rotational motion. A vector quantity, the angular momentum about an axis of rotation, has a direction perpendicular to the plane containing the momentum and a magnitude equal to the product of the momentum and the line of momentum's perpendicular distance from the axis of rotation. The entire angular momentum of a rigid body or a system of particles is conserved if there is no external force at work, according to the law of conservation of angular momentum.
FAQ
Q. Is angular motion the same as rotational motion?
Ans. Angular momentum, also referred to as the moment of momentum or rotational momentum, is the rotational equivalent of linear momentum. Because it's a conserved quantity—a system's angular momentum stays constant until it's affected by an external torque—it's significant in physics.
Q. When the work done is zero, what are the two conditions?
Ans. When the displacement is normal to the force direction (θ = 90o) or there is no displacement (S = 0), the work done is zero in both scenarios.
Q. What gives rise to rotational motion?
Ans. A body (a system of particles) about an axis experiences a twist when a torque (the rotational equivalent of force) is applied to it. This twist results in rotational motion. This is only comparable to the situation where a force causes translational motion.
Q. What is the difference between circular and rotational motion?
Ans. When an object goes in a circle, it simply moves in a circle. For instance, artificial satellites orbit the Earth at a fixed altitude. The object rotates in a circular manner around an axis. For instance, the Earth rotates on its own axis.
