Classical Mechanics
39 questions across 3 topics. Also examined in CNET.
Generalized Coordinates, Lagrange's Equations
- 96Mechanics — Euler's theorem on homogeneous parts of TMSET June 2025Generalized Coordinates, Lagrange's EquationsEasy
- 97Mechanics — the energy relation is a consequence, not a restatementMSET June 2025Generalized Coordinates, Lagrange's EquationsMedium
- 98Mechanics — velocity perpendicular to gravity at the topMSET June 2025Generalized Coordinates, Lagrange's EquationsEasy
- 99Mechanics — adding a total time derivative to LMSET June 2025Generalized Coordinates, Lagrange's EquationsEasy
- 95Rotating-frame Lagrangian — the Hamiltonian is conserved, but isn't the energyMSET April 2024Generalized Coordinates, Lagrange's EquationsHard
- 96Lagrange's equation of motion — rate of change of momentumMSET April 2024Generalized Coordinates, Lagrange's EquationsHard
- 97Gauge freedom in the Lagrangian — adding a total time derivativeMSET April 2024Generalized Coordinates, Lagrange's EquationsHard
- 99The simple pendulum — when H and E genuinely coincideMSET April 2024Generalized Coordinates, Lagrange's EquationsMedium
- 98Identifying the Hamiltonian for a reduced (effective) one-coordinate LagrangianMSET March 2023Generalized Coordinates, Lagrange's EquationsHard
- 99Lagrangian for a body falling under gravity (downward-positive coordinate)MSET March 2023Generalized Coordinates, Lagrange's EquationsEasy
- 71Degrees of freedom — the correct constraint-counting formulaMSET September 2021Generalized Coordinates, Lagrange's EquationsMedium
- 73Legendre transform back from a given HamiltonianMSET September 2021Generalized Coordinates, Lagrange's EquationsMedium
- 71Non-holonomic constraints leave the configuration-space dimension unreducedMSET June 2019Generalized Coordinates, Lagrange's EquationsEasy
- 72The momentum conjugate to a cyclic coordinate is conservedMSET June 2019Generalized Coordinates, Lagrange's EquationsEasy
- 53An attractive m/r^2 force has potential -m/r, so L=T+m/rMSET January 2018 Paper IIIGeneralized Coordinates, Lagrange's EquationsEasy
- 54Atwood's machine: (m1+m2)ddot x=(m1-m2)gMSET January 2018 Paper IIIGeneralized Coordinates, Lagrange's EquationsEasy
- 52Velocity in polar coordinates has components dot r and rdotthetaMSET April 2017 Paper IIIGeneralized Coordinates, Lagrange's EquationsEasy
- 53Pendulum: V=mgl(1-costheta) measured from the lowest pointMSET April 2017 Paper IIIGeneralized Coordinates, Lagrange's EquationsEasy
- 55The harmonic oscillator: ddot x+omega^2x=0MSET April 2017 Paper IIIGeneralized Coordinates, Lagrange's EquationsEasy
Hamilton's Canonical Equations, Hamilton's Principle
- 94Mechanics — with air resistance, H is the energy but is not conservedMSET June 2025Hamilton's Canonical Equations, Hamilton's PrincipleMedium
- 95Mechanics — canonical momentum on a parabolaMSET June 2025Hamilton's Canonical Equations, Hamilton's PrincipleMedium
- 94Total energy in Hamiltonian (momentum) form for projectile motionMSET March 2023Hamilton's Canonical Equations, Hamilton's PrincipleEasy
- 95Hamiltonian for a velocity-dependent (non-natural) potentialMSET March 2023Hamilton's Canonical Equations, Hamilton's PrincipleHard
- 96H is conserved even when it fails to equal the total energyMSET March 2023Hamilton's Canonical Equations, Hamilton's PrincipleHard
- 72Canonical momenta from a Lagrangian with a velocity-coupling termMSET September 2021Hamilton's Canonical Equations, Hamilton's PrincipleEasy
- 73The harmonic-oscillator Hamiltonian gives angular frequency k, not k^2MSET December 2020Hamilton's Canonical Equations, Hamilton's PrincipleEasy
- 73Hamilton's equations for H=pq give exponential growth and decayMSET June 2019Hamilton's Canonical Equations, Hamilton's PrincipleEasy
- 55Legendre transform of a pendulum-type LagrangianMSET January 2018 Paper IIIHamilton's Canonical Equations, Hamilton's PrincipleEasy
Motion of Rigid Bodies, Euler's Dynamical Equations, Small Oscillations
- 100Mechanics — the moment of inertia about the x-axisMSET June 2025Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 94Projectile motion with linear air resistanceMSET April 2024Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsHard
- 98Circular motion on a string — energy conservation from the lowest pointMSET April 2024Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsMedium
- 97Speed-squared after time t for oblique projectile motionMSET March 2023Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 100Degrees of freedom of a rigid body with one point fixedMSET March 2023Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 74Finite rotations don't commute; infinitesimal ones doMSET September 2021Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsMedium
- 71Three rigidly-linked particles in space have the 6 degrees of freedom of a rigid bodyMSET December 2020Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsMedium
- 72Kinetic energy in plane polar coordinatesMSET December 2020Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 74Equal transverse moments of inertia make the spin-axis angular velocity constantMSET June 2019Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 52Three coordinates fix a point, three angles fix the orientationMSET January 2018 Paper IIIMotion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy
- 54Euler's theorem: a rigid displacement about a fixed point is a rotationMSET April 2017 Paper IIIMotion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsEasy