Systems of Particles and Rotational Motion

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! Refer to the official website of Vedantu or download the app for an elaborate and comprehensive explanation.

What is a Rigid Body?

Euler’s angle and Euler’s equations have to be introduced in order to describe the attitude of a rigid body and to determine its evolution as a function of its initial angular velocity and applied torques. Students will also recall the transformation matrix between different reference frames.

A rigid body is a body that has a perfectly defined shape that is unchangeable. Also, the distance between the different pairs of rigid bodies cannot be changed. Therefore, it can be said that 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.

Rigid body and rigid body dynamics are concepts that were developed in order to be a solution to a range of problems that are hard to explain with classical physics. A point mass cannot fully explain the motions in rotation of a fan, a potter’s wheel, a top, etc. Wheels and steel rods, deformation, and bending are considered to be negligible and are treated as rigid when dealt with in real life.

The concept of Quantum Mechanics can be said to be based on the foundations of Rigid Body Dynamics. A rigid body can undergo two types of motions namely

• Translational Motion

• Rotational Motion

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.

The Motion of a Rigid Body

The motion of a system of particles and a 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 center 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 illustrations of examples given there. 

Center of Mass

Many problems arise from this subtopic where students are asked to find the center of mass of a system of particles. Let’s briefly understand what it is about. After certain experiments, it was concluded that the center of mass of a system of particles moves like all the mass of the system was concentrated at the center 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 center of mass.

The center of mass can be described as the average position of all the parts of a system or it can be said that it is the mean location of a distribution of mass in space. It is a point where the force is applied which results in linear acceleration without any angular acceleration. Motions of this point are congruent to the motion of a single particle and the mass of this particle is equivalent to the sum of all individual particles of the system by surrounding bodies or action of a field of force is exerted directly to that particle. 

System of Particles and Rotational Motion Formulas

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

1. The position vector of the center of mass

2. In the coordinate system

3. The velocity of the 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 counterclockwise (positive) or clockwise (negative).

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

• Its SI unit is the 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.

• The angular velocity of a particle varies at different points.

• The angular velocity of all the particles of a rigid body is the same as 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

• The pure rolling motion of a sphere/cylinder/disc