Mechanics

What mechanics covers

The largest Year 12 unit, and the one most other units are built on. It covers describing motion, predicting it from the forces acting, and then solving the same problems again with momentum and energy when the forces are unknown. Circular motion, gravitational fields and the engineering physics option all assume you can work through this quickly.

The main ideas

• Scalars and vectors: adding a perpendicular pair by calculation, others by scale drawing, and resolving weight on a slope.
• Moments, couples and the principle of moments, with weight placed at the centre of mass.
• Motion graphs read as gradients and areas, and the four constant-acceleration equations with the condition attached.
• Projectiles as two independent motions linked only by a shared time.
• Newton's three laws applied from a free-body diagram, and what makes a genuine third-law pair.
• Drag and terminal speed, and the same balance argument applied to a vehicle's top speed.
• Momentum, impulse and conservation, then work, energy, power and efficiency, including budgets with friction in them.

The equations it turns on

v = u + at     s = ut + 12at²     v² = u² + 2as     s = 12(u + v)t$v = u + at \qquad s = ut + \tfrac{1}{2}at^{2} \qquad v^{2} = u^{2} + 2as \qquad s = \tfrac{1}{2}(u + v)t$v = u + at s = ut + (1/2)at^2 v^2 = u^2 + 2as s = (1/2)(u + v)t

the four equations, valid only while acceleration is constant

F = ma$F = ma$F = ma

the resultant force on a body of constant mass

p = mv     F = Δ(mv)Δt$p = mv \qquad F = \frac{\Delta(mv)}{\Delta t}$p = mv F = Δ(mv)/Δt

momentum, and the general form of the second law

FΔt = Δ(mv)$F\Delta t = \Delta(mv)$FΔt = Δ(mv)

impulse, the area under a force-time graph

W = Fscos θ     P = Fv$W = Fs\cos\theta \qquad P = Fv$W = Fs cos θ P = Fv

work done by a force, and power at a steady speed

E_k = 12mv²     ΔE_p = mgΔh$E_{k} = \tfrac{1}{2}mv^{2} \qquad \Delta E_{p} = mg\Delta h$E_k = (1/2)mv^2 ΔE_p = mgΔh

the two stores most problems exchange

Where it usually goes wrong

• Weight and the normal contact force are not a third-law pair. They act on the same body and are different types of force, and a pair fails on either count.
• The constant-acceleration equations stop being valid once drag matters. Where acceleration varies, the area under a velocity-time graph gives displacement.
• Momentum is signed, so a direction has to be chosen before anything is conserved, and a two-dimensional collision must be resolved into components.
• Momentum is conserved in every collision, kinetic energy only in an elastic one, so deciding the type takes a separate energy audit.

Where to start

Start with scalars and vectors, then motion graphs and SUVAT, since projectiles use both. Newton's laws, mass and weight and drag follow as one group. Leave momentum and energy last: they reuse everything before them and carry the longest questions.