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Class 12 Physics - Mechanics: Core Formulas
Vectors
- Magnitude: |A| = sqrt(Ax^2 + Ay^2 + Az^2)
- Dot product: A·B = AB cosθ = AxBx + AyBy + AzBz
- Cross product: A×B = |A||B| sinθ n̂ (right-hand rule)
- Unit vector: û = A/|A|
Work & Energy
- Work: W = F·s = ∫F·ds (J)
- Kinetic energy: K = 1/2 mv^2
- Potential energy (gravity): U = mgh
- Work–energy theorem: W_net = ΔK
- Power: P = dW/dt = F·v (W)
Rotation
- Angular displacement: θ (rad)
- Angular velocity: ω = dθ/dt
- Angular acceleration: α = dω/dt
- Relation to linear: v = ωr, a_t = αr, a_c = ω^2 r
- Torque: τ = r×F = Iα
- Moment of inertia (common): I_cm (rod about center)= (1/12) mL^2; (solid disc)= (1/2) mR^2; (thin hoop)= mR^2
- Rotational kinetic energy: K_rot = 1/2 Iω^2
- Work by torque: W = ∫τ dθ
Conservation
- If only conservative forces: E_total = K + U = constant
- Angular momentum: L = Iω, conserved if τ_ext = 0
Exam Tip
- Memorize formula forms and units; draw a quick free-body & rotation diagram,
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