System of Particles and Rotational Motion

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A rigid body is an idealized body with a perfectly definite and unchanging shape where distances between all pairs of particles remain constant. Although no real body is truly rigid, objects like a st…

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1. Pure Translation: All particles of the body move with the same velocity at any instant (e.g., a block sliding down an inclined plane) 2. Rotation: The body rotates about a fixed axis, with each par…

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The center of mass is the point where the entire mass of the system can be considered to be concentrated for analyzing translational motion. For n particles: R = (Σmᵢrᵢ)/M Where: - R = position vect…

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MA = F_ext Where: - M = total mass of the system - A = acceleration of center of mass - F_ext = sum of all external forces This means the center of mass moves as if all the mass were concentrated at…

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Linear momentum of a system: P = Σpᵢ = Σmᵢvᵢ Relation to center of mass: P = MV Where: - P = total linear momentum - M = total mass - V = velocity of center of mass This shows that the total moment…

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If the sum of external forces acting on a system of particles is zero, then the total linear momentum of the system remains constant. Mathematically: If F_ext = 0, then P = constant This also means …

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Vector product a × b is a vector c with: 1. Magnitude: |c| = ab sin θ 2. Direction: Perpendicular to both a and b (right-hand rule) 3. Properties: - Not commutative: a × b = -b × a - Distributi…

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Angular velocity (ω) is the rate of change of angular displacement: ω = dθ/dt Relation to linear velocity: v = ω × r For rotation about a fixed axis: v = ωr Where: - v = linear velocity of particle…