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).