Dynamics
Dynamics
The FE Mechanical dynamics items test kinematics, Newton's second law, work-energy, impulse-momentum, and rigid-body motion. Many problems can be solved with more than one method; choose the one that matches the given and requested quantities to save time.
Core rules and concepts
- Rectilinear motion: v = ds/dt, a = dv/dt = v dv/ds. For constant acceleration: v = v0 + at, s = s0 + v0t + ½at², v² = v0² + 2a(s - s0).
- Curvilinear motion: normal acceleration a_n = v²/ρ toward the center of curvature; tangential acceleration a_t = dv/dt.
- Projectile motion: horizontal acceleration is zero; vertical acceleration is -g when air resistance is neglected.
- Newton's second law: ΣF = ma. For rotation about the mass center, ΣM_G = I_G α.
- Work-energy: T1 + U1→2 = T2. Translation kinetic energy is ½mv²; rotation kinetic energy is ½Iω². Conservative potential energy includes mgh and ½kx².
- Impulse-momentum: ∫F dt = Δp. Angular impulse changes angular momentum. Momentum is conserved only when the net external impulse is zero.
- Rigid-body kinematics: v_P = v_G + ω × r and a_P = a_G + α × r - ω²r.
Worked example
A 5 kg block starts from rest and slides 4 m down a 30° incline with μ_k = 0.2. Use work-energy. Gravity work = mg sin30°(4) = 5(9.81)(0.5)(4) = 98.1 J. Normal force N = mg cos30° = 5(9.81)(0.866) = 42.5 N. Friction force = 0.2(42.5) = 8.5 N, and friction work = -8.5(4) = -34.0 J. Net work = 64.1 J = ½(5)v², so v² = 25.64 and v = 5.06 m/s.
Traps that cost marks
- Using static friction when the block is already sliding.
- Omitting the normal force on an incline when computing friction.
- Confusing normal and tangential acceleration.
- Forgetting that friction work is negative.
- Applying conservation of momentum when an external impulse acts.
- Mixing units such as grams and kilograms in kinetic energy.