ANALYTICAL MECHANICS PRACTICE
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
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1. Which principle states that the actual path of a system makes the action
stationary?
A. Newton’s second law
B. D’Alembert’s principle
C. Hamilton’s principle
D. Least force principle
Answer: C
Rationale: Hamilton’s principle states that the action integral is stationary
for the true path.
2. The Lagrangian of a system is defined as
A. T + V
B. T − V
C. V − T
D. T/V
Answer: B
Rationale: The Lagrangian is kinetic energy minus potential energy.
3. Generalized coordinates are
A. Always Cartesian
B. Always angles
C. Any independent variables describing configuration
, D. Only linear displacements
Answer: C
Rationale: Generalized coordinates can be any convenient independent
variables.
4. The Euler–Lagrange equation is derived from
A. Newton’s laws
B. Calculus of variations
C. Vector algebra
D. Hamiltonian dynamics
Answer: B
Rationale: It follows from minimizing (or extremizing) the action.
5. A cyclic coordinate is one that
A. Is periodic
B. Has zero velocity
C. Does not appear in the Lagrangian
D. Has constant acceleration
Answer: C
Rationale: If a coordinate does not appear explicitly, it is cyclic.
6. The conjugate momentum is defined as
A. ∂L/∂q
B. ∂L/∂q̇
C. dq/dt
D. ∂T/∂q
Answer: B
Rationale: Conjugate momentum is the derivative of the Lagrangian with
respect to velocity.
7. Conservation of momentum arises from
A. Energy invariance
B. Rotational symmetry
C. Translational symmetry
D. Time symmetry
, Answer: C
Rationale: Noether’s theorem links translational symmetry to momentum
conservation.
8. Conservation of energy corresponds to
A. Spatial symmetry
B. Time invariance of the Lagrangian
C. Rotational symmetry
D. Gauge invariance
Answer: B
Rationale: Time translation symmetry implies energy conservation.
9. The Hamiltonian is defined as
A. T − V
B. Σ pᵢq̇ ᵢ − L
C. V − T
D. Σ qᵢṗᵢ
Answer: B
Rationale: The Hamiltonian is obtained via Legendre transformation.
10.In many systems, the Hamiltonian equals
A. Potential energy
B. Kinetic energy
C. Total energy
D. Action
Answer: C
Rationale: When L has no explicit time dependence and T is quadratic in
velocities, H = E.
11.Phase space has dimensions
A. n
B. 2n
C. 3n
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
DOWNLOAD PDF
1. Which principle states that the actual path of a system makes the action
stationary?
A. Newton’s second law
B. D’Alembert’s principle
C. Hamilton’s principle
D. Least force principle
Answer: C
Rationale: Hamilton’s principle states that the action integral is stationary
for the true path.
2. The Lagrangian of a system is defined as
A. T + V
B. T − V
C. V − T
D. T/V
Answer: B
Rationale: The Lagrangian is kinetic energy minus potential energy.
3. Generalized coordinates are
A. Always Cartesian
B. Always angles
C. Any independent variables describing configuration
, D. Only linear displacements
Answer: C
Rationale: Generalized coordinates can be any convenient independent
variables.
4. The Euler–Lagrange equation is derived from
A. Newton’s laws
B. Calculus of variations
C. Vector algebra
D. Hamiltonian dynamics
Answer: B
Rationale: It follows from minimizing (or extremizing) the action.
5. A cyclic coordinate is one that
A. Is periodic
B. Has zero velocity
C. Does not appear in the Lagrangian
D. Has constant acceleration
Answer: C
Rationale: If a coordinate does not appear explicitly, it is cyclic.
6. The conjugate momentum is defined as
A. ∂L/∂q
B. ∂L/∂q̇
C. dq/dt
D. ∂T/∂q
Answer: B
Rationale: Conjugate momentum is the derivative of the Lagrangian with
respect to velocity.
7. Conservation of momentum arises from
A. Energy invariance
B. Rotational symmetry
C. Translational symmetry
D. Time symmetry
, Answer: C
Rationale: Noether’s theorem links translational symmetry to momentum
conservation.
8. Conservation of energy corresponds to
A. Spatial symmetry
B. Time invariance of the Lagrangian
C. Rotational symmetry
D. Gauge invariance
Answer: B
Rationale: Time translation symmetry implies energy conservation.
9. The Hamiltonian is defined as
A. T − V
B. Σ pᵢq̇ ᵢ − L
C. V − T
D. Σ qᵢṗᵢ
Answer: B
Rationale: The Hamiltonian is obtained via Legendre transformation.
10.In many systems, the Hamiltonian equals
A. Potential energy
B. Kinetic energy
C. Total energy
D. Action
Answer: C
Rationale: When L has no explicit time dependence and T is quadratic in
velocities, H = E.
11.Phase space has dimensions
A. n
B. 2n
C. 3n
