Important Questions on Systems of Particles and Rotational Motion (Class 11)

1. What is a system of particles?
A system of particles refers to a collection of multiple particles that interact with each other. These particles can have mass and can be stationary or in motion. The motion and behavior of the system as a whole can be analyzed using principles of physics.

2. What are the types of systems of particles?
There are two types of systems of particles:

- Isolated System: In an isolated system, no external forces or torques act on the system. The total momentum and angular momentum of an isolated system are conserved.
- Non-Isolated System: In a non-isolated system, external forces and torques may act on the system, resulting in changes in momentum and angular momentum.

3. What is the center of mass?
The center of mass of a system of particles is the point at which the entire mass of the system can be assumed to be concentrated. It is the average position of all the particles in the system, taking into account their respective masses.

4. How is the center of mass calculated?
The center of mass of a system can be calculated using the following formula:

\[
\text{Center of Mass} = \frac{{m_1 \cdot \vec{r}_1 + m_2 \cdot \vec{r}_2 + \ldots + m_n \cdot \vec{r}_n}}{{m_1 + m_2 + \ldots + m_n}}
\]

where \(m_1, m_2, \ldots, m_n\) are the masses of the particles and \(\vec{r}_1, \vec{r}_2, \ldots, \vec{r}_n\) are their respective positions.

5. What is rotational motion?
Rotational motion refers to the motion of an object around a fixed axis. It involves the rotation of an object, where different points on the object move in circles around the axis of rotation.

6. What is moment of inertia?
The moment of inertia of an object is a measure of its resistance to rotational motion. It depends on both the mass distribution and the axis of rotation. The moment of inertia is denoted by the symbol "I" and is given by the sum of the products of the masses and their distances squared from the axis of rotation.

7. How is the moment of inertia calculated?
The moment of inertia of an object can be calculated using different formulas depending on the shape and distribution of mass. For example:
- For a point mass rotating about an axis:
\[
I = m \cdot r^2
\]
where "m" is the mass and "r" is the perpendicular distance from the axis of rotation.
- For a rigid body rotating about a fixed axis:
\[
I = \sum m_i \cdot r_i^2
\]
where the sum is taken over all the particles in the object and \(r_i\) is the perpendicular distance of each particle from the axis of rotation.

8. What is angular momentum?
Angular momentum is a measure of the rotational motion of an object. It is defined as the product of the moment of inertia and the angular velocity of the object. Angular momentum