Mechanics: rotation, oscillation and fluids
Mechanics: rotation, oscillation and fluids
NEB Class 12 Mechanics tests rigid-body rotation, simple harmonic motion and fluid statics. Expect numericals on moment of inertia, torque, angular momentum, pendulum or spring-mass period, pressure and buoyancy, plus short conceptual explanations.
Core rules
- For a fixed axis, τ = Iα; angular momentum L = Iω is conserved when external torque is zero.
- Moment of inertia depends on axis: disc about centre I = ½MR², solid sphere I = ⅖MR², rod about centre I = ML²/12.
- SHM: a = −ω²x, T = 2π√(m/k), and for a simple pendulum T = 2π√(l/g) for small angles.
- Fluid pressure increases with depth: p = p₀ + ρgh; buoyant force equals weight of displaced fluid.
Worked example
A uniform disc of mass 4.0 kg and radius 0.50 m is free to rotate about its centre. A tangential force gives torque 2.0 N m. Find angular acceleration and tangential acceleration at the rim. I = ½MR² = 0.5 × 4.0 × (0.50)² = 0.50 kg m². α = τ/I = 2.0/0.50 = 4.0 rad s⁻². At rim, a_t = αR = 4.0 × 0.50 = 2.0 m s⁻². The direction is tangential; there is also centripetal acceleration if rotating.
Traps
Using radius as diameter; adding moments of inertia about different axes; treating angular velocity as constant when torque acts; using degrees in ω = 2π/T; forgetting gauge vs absolute pressure; saying buoyant force depends on object density rather than displaced-fluid weight.