# Systems of Particles and Rotational Motion

## System of Particles and Rotational Motion Class 11

This System of Particles and Rotational Motion class 11 chapter comprises many problems for students in examinations. It is important to understand this topic of Physics Chapter 7 to score well in every test. In this article, we will discuss some of the important parts of this topic. Let’s get started!

### What is a Rigid Body?

A rigid body is a body that has a perfect defined shape which is unchangeable. Also, the distance between the different pairs of a rigid body cannot be changed. Therefore, it can be said that the no real body is truly rigid as most of these deform under the influence of forces. However, situations exist where deformations are negligible. The objects which can be considered rigid by neglecting that they wrap/bend/vibrate are wheels, steel, beams, molecules and planets. Further, we are discussing the kind of motion a rigid body can have, this subtopic is also covered in the system of particles class 11 Physics chapter.

### Motion of a Rigid Body

The motion of a system of particles and rigid body can be explained with the help of a few examples.

1. Rectangular Block

Consider a rectangular block that is sliding down on an inclined place without any sidewise movement. It is a rigid body and its motion down the plane is in a manner that all the body particles are moving together. It means all the particles have the same velocity at any instant of time. Thus, this rigid body is in a pure translational motion here. It can be concluded that at any instant of time, in pure translational motion, all particles of the body have the same velocity.

2. Solid Metallic or Wooden Cylinder

Here, we take the rolling motion of a solid metallic/wooden cylinder down the similar inclined plane as discussed above. The cylinder is a rigid body here and it shifts from the top to the bottom of the inclined plane and thus exhibits translational motion. But here, all the particles of this body do not move with the same velocity at any instant of time. Thus, the cylindrical body is not in pure translation. Something else is there in addition to the translation motion.

This something else can be understood by constraining a rigid body so that it won’t be having any translational motion. We can fix it along a straight line (axis of rotation) and the only kind of motion it can display is rotation. For example, in a ceiling fan or a potter’s wheel.

Rotation: When a rigid body is about a fixed axis, every particle of the body moves in a circular motion, and it lies in a plane perpendicular to the axis having its centre on the axis, it is called rotation.

All of these points are well covered in rotational motion physics class 11 chapter 7 NCERT books. Students can have a deeper understanding by seeing different figures and illustration of examples given there.

### Centre of Mass

Many problems arise from this subtopic where students are asked to find the centre of mass of a system of particles. Let’s briefly understand what it is about. After certain experiments, it was concluded that the centre of mass of a system of particles moves like all the mass of the system was concentrated at the centre of it and all the external forces were applied at the central point. Also, it was known that the total momentum of a system of particles is equal to the product of the total mass of the body or system and the velocity of its centre of mass.

### System of Particles and Rotational Motion Formulas

The formulas for the following terms are known in this topic-

1. Position vector of center of mass

2. In coordinate system

3. Velocity of Center of mass

4. Force

5. Momentum conservation in Centre of Mass motion

### Understanding Rigid Body Dynamics

Angular Displacement

• When a rigid body rotates about a fixed axis, the angle displaced by a line passing through a point on that body and intersecting the axis of rotation perpendicularly is the angular displacement.

• It can be counter clockwise (positive) or clockwise (negative).

• It is analogous to a component of the displacement vector.

• Its SI unit is radian. Other units include degree and revolution.

Angular Velocity

• It is the average angular velocity and can be negative or positive.

• It is a vector quantity and the direction is perpendicular to the plane of rotation.

• Angular velocity of a particle varies about different points.

• Angular velocity of all the particles of a rigid body is the same about a point.

• It represents the speed (how fast) of an object rotating or revolving relative to another point or the speed at which the angular position or orientation of a body changes with time.

Besides these, System of Particles and Rotational Motion Class 11 NCERT books covers various other terms and important formula for chapter 7 Physics that include:

• Angular Acceleration

• Vector nature of angular variables

• Kinematics of rotational motion

• Relation between linear and angular variables

• Moment of inertia

• Parallel Axis Theorem

• Perpendicular Axis Theorem

• Torque

• Rotational Kinetic Energy

• Rotational Work Done

• Power

• Angular Momentum

• Law of conservation on angular momentum

• Angular impulse

• Equilibrium of a rigid body

• Pure rolling motion of a sphere/cylinder/disc