Dynamics, Kinematics and Vibrations is 10-15 questions on the FE Mechanical exam, tying it with Fluid Mechanics, Thermodynamics and Mechanical Design as the heaviest area on the paper. On the FE Civil exam the equivalent area is worth 4-6. That difference is the single biggest gap between the two disciplines.
It is also where method selection matters most. The same problem can take forty seconds by work-energy or six minutes by integrating accelerations, and choosing badly is how candidates run out of time on the second half of the exam.
Exam weight: NCEES lists Dynamics, Kinematics, and Vibrations at 10-15 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Dynamics, Kinematics, and Vibrations
The specification covers kinematics of particles and rigid bodies, mass moment of inertia, force-acceleration relationships, work-energy methods, impulse-momentum including impact, and free and forced vibration. Expect projectile motion, a rolling body on an incline, a collision with a coefficient of restitution, and a spring-mass system's natural frequency.
Vibration items are the ones mechanical candidates most often meet for the first time on the exam. Undamped natural frequency, damping ratio and resonance appear as short computations or as concept questions about what happens when forcing frequency approaches natural frequency.
5 Free Dynamics, Kinematics, and Vibrations Practice Problems
Each dynamics problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — B. Kinetic friction
A 150-lb crate slides on a horizontal floor with a coefficient of kinetic friction \(\mu_k\) = 0.35. The kinetic friction force (lb) acting on the crate is most nearly:
Answer: D) 52.5
Refer to the Kinetics section in the Dynamics chapter of the FE Reference Handbook.
On a horizontal surface, the normal force equals the weight:
\(N = W = 150 lb\)
Kinetic friction force:
\(\boxed{Fk = \mu_k \times N = 0.35 \times 150 = 52.5 lb}\)
Problem 2 — C. Newton's second law for particles
A 1000 kg elevator accelerates upward at 2 \(\text{m/s}^{2}\). What is the tension in the cable? (g = 10 \(\text{m/s}^{2}\))
Answer: C) 12,000 N
Free body diagram: Tension T (up), Weight W = mg (down)
\(\Sigma F = ma\) (taking upward as positive)
$$T - mg = ma$$
\(T = m(g + a) = 1000(10 + 2) = 12,000\) N
The tension must overcome both gravity and provide acceleration.
Problem 3 — G. Kinematics of mechanisms
A slider-crank mechanism has a crank of length 100 mm rotating at 100 rad/s and a connecting rod of length 300 mm. When the crank angle is 90 degrees from top dead center as shown in the figure, the velocity (m/s) of the piston is most nearly:
Answer: B) 10.0
Refer to the Rigid Body Dynamics section in the Dynamics chapter of the FE Reference Handbook.
The approximate piston velocity for a slider-crank is:
\(vB = r \times \omega \times (\sin(\theta) + (r/(2 \times L)) \times \sin(2 \times \theta))\)
At theta = 90 degrees:
\(\sin(90) = 1, \sin(180) = 0\)
$$\boxed{vB = 0.1 \times 100 \times (1 + 0) = 10.0 m/s}$$
Problem 4 — H. Newton's second law for rigid bodies
A uniform sphere (m = 5 kg, r = 0.2 m) rolls without slipping on a horizontal surface under a horizontal force of 10 N applied at its center. What is the acceleration?
Answer: C) 1.43 \(\text{m/s}^{2}\)
For a solid sphere: \(I = \frac{2}{5}mr^2\)
Rolling constraint: \(a = r\alpha\)
Force equation: \(F - f = ma\) ... (1)
Moment equation: \(fr = I\alpha = \frac{2}{5}mr^2 \cdot \frac{a}{r} = \frac{2}{5}mra\)
\(f = \frac{2}{5}ma\) ... (2)
Substitute (2) into (1):
\(F = ma + \frac{2}{5}ma = \frac{7}{5}ma\)
\(a = \frac{5F}{7m} = \frac{5(10)}{7(5)} = \frac{50}{35} = 1.43\) m/s\(^{2}\)
Problem 5 — D. Work-energy of particles
A 5-kg package is released from rest on a smooth ramp at point A (height 3 m) and slides down to point B where it encounters a spring with k = 2000 N/m as shown in the figure. The maximum compression (m) of the spring is most nearly: (g = 9.81 m/s\(^2\))
Answer: D) 0.384
Refer to the Work and Energy section in the Dynamics chapter of the FE Reference Handbook.
Conservation of energy (no friction):
\(mg \times h = (1/2) \times k \times x^2\)
\(5(9.81)(3) = (1/2)(2000) \times x^2\)
\(147.15 = 1000 \times x^2\)
\(x^2 = 0.14715\)
\(\boxed{x = 0.384 m}\)
Using the FE Reference Handbook for Dynamics, Kinematics, and Vibrations
The Dynamics section carries the kinematic equations, the mass moment of inertia table for standard bodies, and the vibration relationships. The mass moment table is easy to confuse with the area moment table in Statics, and they are different quantities with different units. Confirm which one you are reading before you substitute, because the two tables sit close together in the handbook.
Four Mistakes That Cost Points
- Integrating when work-energy would do. If a question gives you positions and speeds but no time, work-energy is almost certainly the intended route. Reaching for kinematic equations instead converts a one-line problem into a multi-step one and often needs information you were not given.
- Using area moment of inertia in a rotation problem. Rotational dynamics needs mass moment of inertia. Pulling the area moment from the statics table produces a plausible number with the wrong units and the wrong magnitude.
- Forgetting the rolling constraint. For a body rolling without slipping, velocity of the centre equals radius times angular velocity. Treating translation and rotation as independent leaves the problem underdetermined or gives a distractor answer.
- Applying conservation of energy across an impact. Momentum is conserved in a collision; kinetic energy is not, unless the impact is perfectly elastic. Use the coefficient of restitution the question provides rather than assuming energy is preserved.
Frequently Asked Questions
How many dynamics questions are on the FE Mechanical exam?
NCEES specifies 10-15 questions from Dynamics, Kinematics and Vibrations out of 110. It is tied for the largest knowledge area on the exam alongside Fluid Mechanics, Thermodynamics and Mechanical Design and Analysis.
How much vibration content is actually tested?
Enough to matter. Expect natural frequency of a spring-mass system, the effect of damping, and the concept of resonance. Full modal analysis and multi-degree-of-freedom systems are outside the scope, so a focused afternoon on single-degree-of-freedom vibration covers most of what appears.
When should I use impulse-momentum instead of work-energy?
Use impulse-momentum when the question involves time, an impact, or a change in velocity over a stated duration. Use work-energy when it involves distance, height or spring compression. If the problem mentions a collision, momentum is conserved and energy generally is not.
Is FE Mechanical dynamics harder than FE Civil dynamics?
It is broader rather than deeper. FE Civil covers particle kinematics and basic rigid-body motion at 4-6 questions. FE Mechanical adds vibrations and more rigid-body work at 10-15 questions, so the area demands substantially more preparation time.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Statics practice problems — 9-14 questions on the exam
- FE Mechanical Mechanical Design and Analysis practice problems — 10-15 questions on the exam
- FE Mechanical Mathematics practice problems — 6-9 questions on the exam
Done with dynamics? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.