Mechanics and Motion
Mechanics and Motion is the largest single block of the GTLE Subject Specialism Physics paper. Items test whether you can move fluently between the three descriptions of motion - kinematics (what happens), dynamics (why it happens) and conservation laws (what stays the same) - and apply them to vehicles, pulleys, inclined planes, projectiles and rotating bodies.
Core rules
- The five SUVAT equations (v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; s = vt − ½at²) hold only for constant acceleration in a straight line.
- Newton's second law is a vector statement, ΣF = ma, applied separately per direction - which is why a free-body diagram must come before the algebra.
- Momentum is conserved in every collision or explosion where external forces are negligible; impulse Ft = Δ(mv) explains airbags, crumple zones and giving with the hands when catching.
- Mechanical energy is conserved only when gravity or springs are the sole agents doing work. With friction, use the work–energy theorem: net work = change in kinetic energy.
- Circular motion requires a resultant force towards the centre of magnitude mv²/r. Centripetal force is not an extra force; it is supplied by tension, friction, gravity or a normal reaction.
- A rigid body is in equilibrium when both the net force and the net moment about any point are zero; a couple produces rotation without translation.
Worked example
A 2.0 kg block is released from rest and descends a vertical height of 1.8 m down a smooth incline of angle 30°. Find its speed at the bottom. Kinematics route: acceleration along a smooth slope is g sin 30° = 4.9 m/s²; the distance along the slope is 1.8 / sin 30° = 3.6 m; then v² = 0 + 2(4.9)(3.6) = 35.3, so v ≈ 5.9 m/s. Energy route, which is faster and shows why the mass cancels: mgh = ½mv², so v = √(2 × 9.8 × 1.8) ≈ 5.9 m/s. If the slope were rough you would need mgh − W_friction = ½mv².
Traps that cost marks
- Confusing mass (kg, scalar, constant) with weight (N, vector, g-dependent).
- Drawing a separate 'centripetal force' arrow on top of the tension that already provides it.
- Applying SUVAT across a point where acceleration reverses, such as a ball thrown upwards.
- Forgetting the normal reaction when computing friction: F = μR, not μmg on an incline.
- Losing signs for deceleration, or switching positive direction mid-question.
- Quoting more significant figures than the data support.