Chapters

1 · Formulas and when each holds

• τ = r × F, with r from the point the torque is taken about.
• τ = Iα about a fixed axis, or about the centre of mass.
• L = Iω about a fixed axis; L is conserved when the net external torque is zero.
• Rolling without slipping: v = ωR, KE = ½mv²(1 + k²/R²).
• Parallel axis: I = I_cm + Md².

2 · Question types and the first step

• Rolling down an incline: write a = g sin θ / (1 + k²/R²) first.
• Collision with a rod: conserve angular momentum about the pivot, not linear momentum.

3 · Traps

Parallel axis: d is the distance between parallel axes, never along the axis.

Torque about a point: he took r from the axis instead of from the point asked about. Rule: mark the point first, draw r from it.

4 · My additions

• Draw the axis before writing any I.

1 · Formulas and when each holds

• pH = −log[H⁺]; pH + pOH = 14 at 25 °C.
• Weak acid: [H⁺] = √(Ka·C), when the degree of dissociation is small.
• Buffer (Henderson): pH = pKa + log([salt]/[acid]).
• Salt of weak acid and strong base: pH = 7 + ½(pKa + log C).

2 · Question types and the first step

• Buffer questions: find the ratio of salt to acid before anything else.
• Solubility product: write s in terms of Ksp from the formula of the salt.

3 · Traps

Common ion: solubility falls in a solution that already holds one of the ions.

Buffer on dilution: he diluted the acid alone. Rule: dilution changes salt and acid equally, so the ratio and the pH stay.

4 · My additions

• Check the temperature before using 14.

1 · Formulas and when each holds

• Bond order (MOT) = ½(bonding − antibonding electrons).
• Hybridisation: count σ bonds and lone pairs on the central atom.
• Dipole moment is a vector: symmetric shapes cancel.

2 · Question types and the first step

• Shape questions: count electron pairs, then name the geometry, then the shape.
• Magnetic behaviour: write the MO filling and look for unpaired electrons.

3 · Traps

O₂ is paramagnetic: two unpaired electrons in π* orbitals.

4 · My additions

• s-p mixing changes the order for B₂, C₂, N₂.

1 · Formulas and when each holds

• AP: aₙ = a + (n − 1)d; Sₙ = n/2 (2a + (n − 1)d).
• GP: aₙ = arⁿ⁻¹; Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1; S∞ = a/(1 − r) when |r| < 1.
• AM ≥ GM ≥ HM for positive numbers, equal only when all are equal.

2 · Question types and the first step

• Terms given in a GP: write them as a/r, a, ar.
• Sum of a series with a pattern in the differences: find the general term first.

3 · Traps

S∞: only when |r| < 1; check before using it.

4 · My additions

• For three terms in AP, take a − d, a, a + d.