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Dynamics, Kinematics, and Vibrations practice questions

10 free Dynamics, Kinematics, and Vibrations questions for the FE Mechanical Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

One of the four largest domains: motion of particles and rigid bodies, the forces that cause it, and free and forced vibration.

Exam weight
10%
On a real exam
≈ 11 questions
In our bank
60 questions

Topics that come up most

  • Kinematics of particles and rigid bodies
  • Newton's second law for translation and rotation
  • Work-energy methods
  • Impulse, momentum and impacts
  • Natural frequency and damped or forced vibration

How to study it

For each problem, decide first whether force, energy or momentum is the quickest route; practise choosing before solving.

Sample Dynamics, Kinematics, and Vibrations questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    A uniform slender rod of mass 3 kg and length 2 m pivots about one end. What is its mass moment of inertia about the pivot?

    • A4 kg·m²
    • B1 kg·m²
    • C12 kg·m²
    • D13 kg·m²
    Show answer and explanation

    Answer: A) 4 kg·m²

    About one end, a slender rod has I = mL²/3 (equivalently mL²/12 + m(L/2)²), so I = 3(4)/3 = 4 kg·m².

    • ACorrect. For a slender rod about one end, I = mL²/3 = 3(2²)/3 = 4 kg·m². This equals the centroidal value plus m(L/2)².
    • BIncorrect. This is mL²/12 = 3(4)/12, the moment of inertia about the rod's center, not about its end.
    • CIncorrect. This is mL², which treats the whole mass as a point at the far end. That overstates the inertia of a uniform rod.
    • DIncorrect. This applies the parallel-axis theorem with a distance of L (1 + 3·2²) instead of L/2. The correct value is 1 + 3(1)² = 4 kg·m².

  2. Question 2

    A 0.5-kg ball of clay moving horizontally at 20 m/s strikes and sticks to a 1.5-kg cart at rest on a frictionless horizontal track. What is the speed of the cart and clay right after impact?

    • A6.7 m/s
    • B10.0 m/s
    • C5.0 m/s
    • D15.0 m/s
    Show answer and explanation

    Answer: C) 5.0 m/s

    In a perfectly inelastic collision, linear momentum is conserved: v = m₁v₁/(m₁ + m₂) = 10/2.0 = 5.0 m/s.

    • AIncorrect. This divides the initial momentum (10 kg·m/s) by the cart's mass alone (1.5 kg). After impact the clay moves with the cart, so the total mass is 2.0 kg.
    • BIncorrect. This assumes kinetic energy is conserved (100 J = ½(2.0)v²). In a perfectly inelastic collision, kinetic energy is lost and only momentum is conserved.
    • CCorrect. Momentum is conserved: (0.5)(20) = (0.5 + 1.5)v, so v = 10/2.0 = 5.0 m/s.
    • DIncorrect. This multiplies the initial speed by the wrong mass ratio, m_cart/(m_total) = 1.5/2.0, instead of m_clay/(m_total) = 0.5/2.0.

  3. Question 3

    A projectile is launched at 20 m/s at 30° above level ground. Neglecting air resistance, its maximum height is about:

    • A15.3 m
    • B20.4 m, using the full launch speed
    • C10.2 m, omitting the 2 in the denominator
    • D5.1 m
    Show answer and explanation

    Answer: D) 5.1 m

    • AIncorrect. That isn't the calculation.
    • BIncorrect. Use only the vertical component.
    • CIncorrect. The formula divides by 2g.
    • DCorrect. \((v\sin\theta)^2/(2g)\).

  4. Question 4

    A thin uniform rod has mass 3 kg and length 2 m. Its mass moment of inertia about its center is:

    • A12 kg·m²
    • B4 kg·m²
    • C1 kg·m²
    • D2 kg·m²
    Show answer and explanation

    Answer: C) 1 kg·m²

    • AIncorrect. Divide by 12.
    • BIncorrect. That's about one end (\(mL^2/3\)).
    • CCorrect. \(mL^2/12 = 3(4)/12\).
    • DIncorrect. Recheck the formula.

  5. Question 5

    A car at 20 m/s brakes at a constant 5 m/s². Its stopping distance is:

    • A100 m
    • B80 m
    • C4 m
    • D40 m
    Show answer and explanation

    Answer: D) 40 m

    • AIncorrect. Recheck the formula.
    • BIncorrect. Include the factor of 2.
    • CIncorrect. That's the stopping time.
    • DCorrect. \(d = v^2/(2a) = 400/10\).

  6. Question 6

    A flywheel with I = 2 kg·m² spins at 10 rad/s. Its rotational kinetic energy is:

    • A20 J
    • B200 J
    • C100 J
    • D10 J
    Show answer and explanation

    Answer: C) 100 J

    • AIncorrect. Square the angular velocity.
    • BIncorrect. Include the ½ factor.
    • CCorrect. \(\tfrac{1}{2}I\omega^2 = \tfrac{1}{2}(2)(100)\).
    • DIncorrect. Recheck the calculation.

  7. Question 7

    A 100-N force acts on a body for 0.5 s. The impulse delivered is:

    • A200 N·s
    • B50 N·s
    • C100 N·s
    • D25 N·s
    Show answer and explanation

    Answer: B) 50 N·s

    • AIncorrect. Multiply, don't divide.
    • BCorrect. Impulse = FΔt.
    • CIncorrect. Multiply by the time.
    • DIncorrect. Recheck the calculation.

  8. Question 8

    A ball dropped from 2 m rebounds to 0.5 m. The coefficient of restitution is:

    • A0.25
    • B0.5
    • C0.75
    • D4.0
    Show answer and explanation

    Answer: B) 0.5

    • AIncorrect. Take the square root.
    • BCorrect. \(e = \sqrt{h_2/h_1} = \sqrt{0.25}\).
    • CIncorrect. Recheck the formula.
    • DIncorrect. That's inverted.

  9. Question 9

    A system with a damping ratio of exactly 1.0 is:

    • AUndamped
    • BUnderdamped and oscillates
    • COverdamped and returns slowly
    • DCritically damped
    Show answer and explanation

    Answer: D) Critically damped

    • AIncorrect. That's ζ = 0.
    • BIncorrect. That's ζ < 1.
    • CIncorrect. That's ζ > 1.
    • DCorrect. It returns to rest fastest without oscillating.

  10. Question 10

    Doubling the stiffness of a spring-mass system, with the same mass, changes its natural frequency by a factor of:

    • A1/2
    • B2
    • C\(\sqrt{2}\)
    • D4
    Show answer and explanation

    Answer: C) \(\sqrt{2}\)

    • AIncorrect. It increases.
    • BIncorrect. Frequency goes with the square root.
    • CCorrect. \(\omega_n = \sqrt{k/m}\).
    • DIncorrect. That's too large.

Dynamics, Kinematics, and Vibrations: FAQs

How much of the FE exam is Dynamics, Kinematics, and Vibrations?

Dynamics, Kinematics, and Vibrations is 10% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 11 questions. The real exam's exact split varies by form.

What does the Dynamics, Kinematics, and Vibrations domain cover?

One of the four largest domains: motion of particles and rigid bodies, the forces that cause it, and free and forced vibration.

How should I study Dynamics, Kinematics, and Vibrations for FE?

For each problem, decide first whether force, energy or momentum is the quickest route; practise choosing before solving.

Where can I practise more Dynamics, Kinematics, and Vibrations questions?

This page has 10 free Dynamics, Kinematics, and Vibrations questions with answers. The ExamWize FE question bank has 60 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Dynamics, Kinematics, and Vibrations exam-ready

The full FE bank has 60 Dynamics, Kinematics, and Vibrations questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice examsTake the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.