### Problem Sessionmotion Of System Of Particles And Rigid Bodies

**Concepts to remember:**

**Center of mass (CoM)**:

- It’s the point where the total mass of an object is concentrated.
- Net external force acts at the CoM.

**Linear momentum (p)**:

- Vector sum of the momenta of all particles in a system.
- Symbol: p = m * v (mass x velocity).
- SI unit: kg m/s.

**Conservation of linear momentum**:

- Total linear momentum remains constant in a closed system.
- Useful in analyzing collisions and explosions.

**Angular momentum (L)**:

- Vector sum of angular momenta of all particles in a system.
- L = I * ω (rotational inertia x angular velocity).
- SI unit: kg m^2/s.

**Conservation of angular momentum**:

- In a closed system, total angular momentum is constant.
- Important in analyzing spinning objects and systems.

**Moment of inertia (I)**:

- Resistance of an object to angular acceleration about an axis.
- Depends on mass distribution and axis of rotation.
- SI unit: kg m^2.

**Parallel axis theorem**:

- Relates the moment of inertia about a parallel axis to that about the CoM.
- I = I_CoM + Md^2 (where M is mass, and d is the distance between axes).

**Perpendicular axis theorem**:

- Relates the moment of inertia about an axis perpendicular to two other axes.
- I = I_x + I_y (where I_x and I_y are moments of inertia about the other axes).

**Rolling motion**:

- Combination of rotation about an axis and translation.
- Involves the concept of the rolling velocity v = ωR (R is the radius).

**Frictional force (f)**:

- Force opposing the relative motion of two surfaces in contact.
- μ = coefficient of friction (f = μN, where N is the normal force).