NCERT Solutions for Class 11 Physics Chapter 6 System of Particles and Rotational Motion

The center of mass is an important property of any rigid body system. The center of gravity represents such a point. As a rule, mechanical systems move in short or rotating motions. In this case, the center of mass also moves and gains speed and acceleration. Let’s see in detail how these metrics are calculated for such a system. If you assume that the mass of an object is at a certain point, you can simplify much of the problem. If the correct location is chosen, the force and motion equations behave the same as they would when applied when the mass is dispersed. This particular location is called the center of gravity. Its position is defined relative to the object or system of objects whose centroid is to be calculated.

Usually for uniform shapes this is their centroid. For symmetrical and uniform shapes, their centers of gravity are located at their centers of gravity. For a ring, its center of mass is inside the ring, which means that an object’s center of mass need not be in the object itself. Consider a multi-particle system. Each part of the system moves at a different speed. Consider a particle system composed of m1, m2, m3, etc. The initial positive vectors of these particles are r1, r2, r3, now these particles start from their positive vector direction, the goal is to find the velocity and direction of velocity at the center of mass of the system.

The motion of an object can be of different types, such as linear motion, circular motion, and rotational motion. According to Newton’s first law of motion, if an object is at rest, it will remain at rest, and if it is in motion, it will remain in motion unless an external force is applied to it. All this is due to the inertia of the body. Linear motion has inertia and rotational motion has a moment of inertia.

Just like linear motion has inertia, rotational motion also has a moment of inertia. This the Newton’s law of motion that a stationary object will stay at rest, while a moving object will keep moving along of a straight line at the same speed, unless an external force acts on it. An object cannot automatically change its potion, but when an external force acts on this object to change its position, this object will oppose it. This tendency of the object is called its inertia. Therefore, a rotating object resists an external moment applied to change its rotational state, a tendency known as the moment of inertia. It is a scalar quantity.

A rigid body is a rigid body with a precisely defined and unchanging shape. The distance between all pairs of particles in an object like this remains the same. Since solid bodies bend under the influence of forces, this definition of rigid body indicates that no solid body is truly rigid. However, in many cases, the deformation is negligible. On the other hand, we can ignore the fact that objects such as wheels, roofs, steel beams, molecules and planets bend (twist), bend or vibrate in various environments and treat them as solids. Rolling is one of the most practiced sports in everyday life. All wheels used in vehicles such as cars, buses, trains, planes, bicycles, buffalo carts, etc. have a rolling motion, and many things have wheels attached like carts.

For clarity, let’s start with a disk as an example, but the results apply to any rolling body rolling on a horizontal surface. Assume the disc does not slip while scrolling. This means that the bottom of the disc in contact with the flat surface is stationary on the surface at a given instant. Rolling motion contains both motions, or it is a combination of translational and rotational motions. The translational motion of an object is the motion of the center of mass. In the rolling motion of an object, the surfaces in contact are slightly deformed. This deformation is temporary, that is, when the surfaces of the two objects touch, the body is temporarily deformed.