System of Particles and Rotational Motion is an important chapter of physics syllabus for class 11. As it includes complex theories, derivations and formulas, it is often regarded as one of the trickiest topics of class 11th. Considering its importance in scholastic as well as competitive examinations, it is vital to understand the intricacies of this chapter. So, let’s get started with the blog and discuss some important pointers of the system of particles and rotation motion.
This Blog Includes:
- Definition of Rigid Body
- What is Centre of Mass?
- Motion of Centre of Mass
- Vector Product of Two Vectors
- Mechanical Equilibrium cases in Rigid body
- Moment of Inertia
- Theorems of System of Particles and Rotational Motion
- Angular Momentum and Law of Conservation Angular Momentum
Definition of Rigid Body
System of Particles and Rotational Motion starts with explaining the concept of a rigid body which is:
- A rigid body is a body for which distances among various particles does not change despite the fact that there are continuous force being applied to them
- A rigid body not fixed can have either translation or a combination of translation and rotation motion
- Angular Velocity remains same for rotating Rigid body for every point at any instance of time
What is Centre of Mass?
Centre of Mass is characterized as the point where the whole mass of the framework is envisioned to be concentrated, for its translational movement. The centre point of mass of a two-molecule framework consistently lies on the line joining the two particles and is someplace in the middle of the particles
Also Read: Types of Motion
Motion of Centre of Mass
The centre point of mass of an arrangement of particles moves as though the whole mass of the framework were amassed at the centre point of mass and all the outside factors are applied at this point. On the off chance that no outside factor follows up on the body, at that point, the focal point of mass will have steady energy. Its speed is steady and acceleration is zero, i.e., MVcm = consistent
Have a look at the Laws of Motion Class 11 study notes!
Vector Product of Two Vectors
The vector or cross result of two vectors a and b is a vector written as a × b. The magnitude of such a vector is ab sin and the direction of the vector is given by the right-hand rule method.
Mechanical Equilibrium cases in Rigid body
In the system of particles and rotational motion chapter, the mechanical equilibrium of a rigid body can be determined by two situations, such as
- If Translational equilibrium is 0
- If Rotational equilibrium is 0 which means total external torque is 0 where torque is defined as a moment of force which is calculated by multiplying immensity of the force being applied on the particle and the perpendicular distance of force from the axis of rotation of the particle
Moment of Inertia
The Moment of inertia of a Rigid body is defined as the rotational inertia of that body. About a given axis, the moment of inertia of a rigid body can be calculated as the sum of the products of the masses of the particles composing the body and the square of their respective perpendicular distance of particles from the axis.
Theorems of System of Particles and Rotational Motion
Chapter 7 of Physics Class 11 System of Particles and Rotational Motion consists of two important theorems which are necessary to understand in order to have a strong grip over this topic. The given theorems are-
The Theorem of Perpendicular Axis
As per this theorem, the moment of inertia I of the body for a given perpendicular axis is always equal to the sum of moments of inertia of the body about two axes always at an angle of 90° to each other in the plane of that body and meeting at a point where the perpendicular axis passes,
I = Ix+Iy
The Theorem of Parallel Axis
According to 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 through the concept of centre of massIcm.
I = Icm+ Ma^2
Angular Momentum and Law of Conservation Angular Momentum
The next important topic in our notes of the system of particles and rotational motion is the Angular Momentum. The angular momentum about an axis of rotation is a vector quantity, whose magnitude is equal to the product of the magnitude of momentum and the perpendicular distance of the line of momentum from the axis of rotation and the direction is perpendicular to the plane containing the momentum. According to the law of conservation of angular momentum, if there is no external force acting, the total angular momentum of a rigid body or a system of particles is conserved.
We hope that this blog on the system of particles and rotational motion notes has helped you in learning more about the topic. Are you confused about which career path to choose after class 12th? Reach out to experts at Leverage Edu.