FE Other Disciplines Dynamics

Knowledge area 9 of the FE Other Disciplines exam: 9–14 of the 110 questions. The subtopics NCEES lists, how they are tested and worked practice problems with solutions.

Take a full timed FE Other Disciplines practice exam

110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

Or start the free Dynamics drill

What the specification lists

  • Particle and rigid-body kinematics
  • Linear motion (e.g., force, mass, acceleration)
  • Angular motion (e.g., torque, inertia, acceleration)
  • Mass moment of inertia
  • Impulse and momentum (e.g., linear, angular)
  • Work, energy, and power
  • Dynamic friction
  • Vibrations (e.g., natural frequency)

From the NCEES FE Other Disciplines CBT exam specifications, knowledge area 9.

Line drawing of a flywheel, a pendulum and a cart rolling down a ramp

How Dynamics is tested

Dynamics questions cover motion of particles and rigid bodies: constant-acceleration kinematics, projectiles, Newton’s second law, work-energy and impulse-momentum. Choose the method from what is given: forces and acceleration point to Newton’s law, speeds and distances to work-energy, times and velocities to impulse-momentum.

On exam day the relationships you need are in the Reference Handbook section on Dynamics. The handbook is the only reference allowed, so practice finding each formula in it rather than memorizing a separate sheet.

Start the free Dynamics drill

FE Other Disciplines Dynamics practice problems

Work each problem with your calculator and the handbook, then open the solution.

Problem 1 · Newton's second law for rigid bodies

A 10 kg block hangs from a light rope wound around a drum of 0.25 m radius. The drum turns in frictionless bearings and has a mass moment of inertia of 2.0 kg·m². Take g = 9.81 m/s². When released, the block's acceleration is most nearly:

  1. A.2.34 m/s²
  2. B.3.07 m/s²
  3. C.5.45 m/s²
  4. D.9.81 m/s²
Show the answer and solution

Answer: A: 2.34 m/s²

Block: mg − T = ma. Drum: Tr = Iα = I(a/r), so T = Ia/r². Combining: a = mg/(m + I/r²) = 98.1/(10 + 32) = 2.34 m/s².

Newton's second law for rigid bodies · Reference Handbook: Dynamics

Problem 2 · Mass moment of inertia

A slender uniform rod has a mass of 3.0 kg and a length of 1.2 m. Its mass moment of inertia about a perpendicular axis through one end is most nearly:

  1. A.0.360 kg·m²
  2. B.1.44 kg·m²
  3. C.4.32 kg·m²
  4. D.4.68 kg·m²
Show the answer and solution

Answer: B: 1.44 kg·m²

I_end = mL²/3 = 3.0(1.2)²/3 = 1.44 kg·m². Equivalently, mL²/12 + m(L/2)² = 0.36 + 1.08 = 1.44 kg·m².

Mass moment of inertia · Reference Handbook: Dynamics

Problem 3 · Impulse-momentum of particles

A 0.15 kg baseball approaching a bat at 40 m/s leaves it at 50 m/s in the opposite direction. The contact lasts 0.0020 s. The average force of the bat on the ball is most nearly:

  1. A.750 N
  2. B.3,000 N
  3. C.3,750 N
  4. D.6,750 N
Show the answer and solution

Answer: D: 6,750 N

Taking the outgoing direction as positive, Δv = 50 − (−40) = 90 m/s. F_avg = mΔv/Δt = 0.15(90)/0.0020 = 6,750 N.

Impulse-momentum of particles · Reference Handbook: Dynamics

Problem 4 · Free and forced vibrations

Select all that apply.

A lightly damped machine on spring mounts has a natural frequency of 28 Hz and is driven by an unbalance at a fixed 30 Hz. The goal is a force transmissibility below 1 (vibration isolation). Which of the following changes achieve that? Select all that apply.

  1. A.Use softer mounts that lower the natural frequency to 15 Hz
  2. B.Add mass so the natural frequency drops to 18 Hz
  3. C.Use stiffer mounts that raise the natural frequency to 30 Hz
  4. D.Use much stiffer mounts that raise the natural frequency to 40 Hz
Show the answer and solution

Answer: A: Use softer mounts that lower the natural frequency to 15 Hz; B: Add mass so the natural frequency drops to 18 Hz

Isolation (transmissibility below 1) requires a frequency ratio r = f/f_n greater than √2 ≈ 1.41. At 15 Hz, r = 2.0; at 18 Hz, r = 1.67; both isolate. At 30 Hz, r = 1 (resonance), and at 40 Hz, r = 0.75, where the transmitted force is amplified.

Free and forced vibrations · Reference Handbook: Dynamics

More FE Other Disciplines practice problems from every knowledge area

Sit the full exam under the real clock

Take a full timed FE Other Disciplines practice exam

110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

Or start the free Dynamics drill

Common questions

How many Dynamics questions are on the FE Other Disciplines exam?

The NCEES FE Other Disciplines specification lists 9–14 questions on Dynamics, out of 110. Every examinee gets the same number per knowledge area.

What does Dynamics cover on the FE Other Disciplines exam?

Particle and rigid-body kinematics; Linear motion (e.g., force, mass, acceleration); Angular motion (e.g., torque, inertia, acceleration); Mass moment of inertia; Impulse and momentum (e.g., linear, angular); Work, energy, and power; Dynamic friction; Vibrations (e.g., natural frequency).

Where are the Dynamics formulas on exam day?

In the NCEES FE Reference Handbook, which appears on screen during the exam: the Dynamics section. Practice with your free copy from MyNCEES so you know where each relationship sits.

Original independent practice questions written to the published NCEES exam specifications. Not affiliated with or endorsed by NCEES (National Council of Examiners for Engineering and Surveying).