**System of Particles and Rotational Motion: Quick Revision Formula**

**1. Introduction to System of Particles and Rotational Motion:**
The branch of physics that deals with the motion of a system of particles and the rotational motion of rigid bodies is known as system of particles and rotational motion. This topic is crucial in understanding the dynamics of objects in rotational motion.

**2. Center of Mass:**
- The center of mass of a system of particles is the point that represents the average position of the particles in the system.
- The center of mass can be calculated using the formula:
Xcm = (m₁x₁ + m₂x₂ + m₃x₃ + ... + mₙxₙ) / (m₁ + m₂ + m₃ + ... + mₙ),
where m₁, m₂, m₃, ..., mₙ are the masses of the particles and x₁, x₂, x₃, ..., xₙ are their respective positions.

**3. Moment of Inertia:**
- The moment of inertia is a measure of an object's resistance to rotational motion around a given axis.
- The moment of inertia of a point mass is given by the formula: I = m*r², where m is the mass and r is the distance from the axis of rotation.
- The moment of inertia of a rigid body can be calculated by integrating the moment of inertia of infinitesimally small mass elements.
- The moment of inertia depends on both the mass distribution and the axis of rotation.

**4. Torque:**
- Torque is the rotational equivalent of force. It is the measure of the tendency of a force to rotate an object about an axis.
- Torque is given by the formula: τ = r x F, where r is the position vector and F is the force applied.
- The torque can also be calculated as the product of force and perpendicular distance from the axis of rotation: τ = r * F * sin(θ).

**5. Angular Momentum:**
- Angular momentum is a vector quantity that measures the rotational motion of an object.
- Angular momentum is given by the formula: L = I * ω, where I is the moment of inertia and ω is the angular velocity.
- Angular momentum is conserved in the absence of external torques.

**6. Kinematics of Rotational Motion:**
- Angular displacement (θ) is given by the formula: θ = ω₀t + 0.5αt², where ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
- Angular velocity (ω) is given by the formula: ω = ω₀ + αt.
- Angular acceleration (α) is given by the formula: α = (ω - ω₀) / t.
- Tangential velocity (v) is given by the formula: v = r * ω, where r is the distance from the axis of rotation.
- Centripetal acceleration (a) is given by the formula: a = r * α, where r is the distance from the axis of rotation.

These are some of the key formulas and concepts related to the system of particles and rotational motion. Understanding and applying these formulas will help in solving problems and analyzing the motion of objects undergoing rotational motion.