Dynamics
4–6 of 110 itemsNCEES draws between 4 and 6 of the 110 from this area on any legal paper. Its outline lists 4 sub-topics; the bank holds 24 verified templates against them, which expand to 700 questions.
Sub-topics, from the NCEES outline
- AKinematics (e.g., particles, rigid bodies)
- BMass moments of inertia
- CForce acceleration (e.g., particles, rigid bodies)
- DWork, energy, and power (e.g., particles, rigid bodies)
5 worked problems
Real questions from the bank, at the depth the exam asks them. Pick an answer first: the reasoning opens when you do, along with why each wrong answer is tempting.
Question 1 of 5
A flywheel turning at 10 rad/s is given a constant angular acceleration of 11 rad/s^2 for 8.5 s. Its angular velocity is most nearly:
Flywheel turning at 10 radians per second and given a constant angular acceleration of 11 radians per second squared. Show the answer and the reasoning
Why D
Given: omega0 = 10 rad/s, alpha = 11 rad/s^2, t = 8.5 s. Relation: omega = omega0 + alpha t, the angular twin of v = v0 + at. Substitute: omega = 10 + 11(8.5). Result: omega = 103.5 rad/s.
Why A is tempting
Left the elapsed time out.
Why B is tempting
Ignored the initial angular velocity.
Why C is tempting
Swapped which quantity is multiplied by time.
Source NCEES FE Reference Handbook 10.6 — Dynamics, Kinematics and Kinetics
Question 2 of 5
A vehicle travelling at 65 ft/s brakes to a stop on a level road with a friction coefficient of 0.5. The stopping distance is most nearly:
Vehicle travelling at 65 feet per second braking to a stop on a level road where the coefficient of friction between the tyres and the surface is 0.5. Show the answer and the reasoning
Why B
Given: v = 65 ft/s, mu = 0.5, level road. Relation: friction gives a deceleration of mu g (the mass cancels), and v^2 = 2as, so s = v^2/(2 mu g). Substitute: mu g = 16.10 ft/s^2; s = 65^2/(2 x 16.10). Result: s = 131.2 ft.
Why A is tempting
Left the friction coefficient out.
Why C is tempting
Dropped the factor of two that comes from v^2 = 2as.
Why D is tempting
Left the acceleration of gravity out.
Source NCEES FE Reference Handbook 10.6 — Dynamics, Kinematics and Kinetics
Question 3 of 5
A body weighing 250 lb has a mass moment of inertia of 16 slug-ft^2 about its mass centre. About a parallel axis 4.5 ft away, it is most nearly:
Show the answer and the reasoning
Why D
Given: Ic = 16 slug-ft^2, m = 250/32.2 = 7.7640 slugs, d = 4.5 ft. Relation: parallel axis theorem, I = Ic + m d^2; the transfer term only ever adds. Substitute: I = 16 + 7.7640(4.5)^2. Result: I = 173.2 slug-ft^2.
Why A is tempting
Subtracted the transfer term. Moving away from the mass centre always increases the moment of inertia.
Why B is tempting
Did not square the transfer distance.
Why C is tempting
Left out the moment of inertia about the mass centre.
Source NCEES FE Reference Handbook 10.6 — Dynamics, Kinematics and Kinetics
Question 4 of 5
A spring with a stiffness of 700 lb/ft is compressed 2.75 ft. The energy stored in it is most nearly:
Show the answer and the reasoning
Why C
Given: k = 700 lb/ft, x = 2.75 ft. Relation: U = (1/2) k x^2, the triangle under the force-deflection line. Substitute: U = 0.5(700)(2.75)^2. Result: U = 2647 ft-lb.
Why A is tempting
Did not square the deflection.
Why B is tempting
Halved the energy a second time.
Why D is tempting
Omitted the factor of one half. The force builds linearly, so the work is the triangle under the force-displacement line.
Source NCEES FE Reference Handbook 10.6 — Dynamics, Kinematics and Kinetics
Question 5 of 5
A projectile leaves the ground at 120 ft/s at 25 degrees above the horizontal. Neglecting air resistance, the horizontal distance it travels before returning to the same elevation is most nearly:
Show the answer and the reasoning
Why C
Given: v = 120 ft/s at theta = 25 degrees, landing at launch elevation, no air resistance. Relation: R = v^2 sin(2 theta)/g. Substitute: R = 120^2 sin(50 deg)/32.2. Result: R = 343 ft. Check: flight time 2v sin(theta)/g = 3.15 s times v cos(theta) = 108.76 ft/s gives the same distance.
Why A is tempting
Reported the maximum height, v^2 sin^2(theta)/2g, rather than the horizontal range.
Why B is tempting
Used sin(theta) instead of sin(2*theta). The range formula carries the double angle.
Why D is tempting
Doubled the range, as if the projectile completed two full arcs.
Source NCEES FE Reference Handbook 10.6 — Dynamics, Kinematics and Kinetics
Four mistakes that cost the question
Each of these lands on an answer that is offered, so it costs the question outright. The minutes are our estimate of the time each one burns on top, against an average of 2.9 minutes a question (320 minutes for 110).
Costs the question and about 2 min
Using weight where the equation wants mass
In US customary units a body weighing 1,500 lb has a mass of 1,500 divided by 32.2, about 46.6 slugs. Using the weight in F = ma makes the acceleration 32.2 times too small, and in kinetic energy makes the energy 32.2 times too large. Convert whenever a stem gives a weight.
Costs the question and about 2 min
Mixing revolutions per minute with radians per second
Angular kinematics needs rad/s: multiply rpm by 2π/60. Using rpm directly puts the answer about 9.5 times too large; dividing by 60 without the 2π leaves it about 6.3 times too small.
Costs the question and about 2 min
Using the centroidal moment of inertia for a rotation about an end
A slender rod's mass moment of inertia is mL²/12 about its centre and mL²/3 about an end. The parallel axis theorem adds md², with d measured from the mass centre and nowhere else. Stopping at mL²/12 gives the factor-of-four distractor.
Costs the question and about 2 min
Leaving speed in miles per hour
Kinematics and energy equations in US units need ft/s, and 1 mph is 1.467 ft/s. Braking distance goes with the square of speed, so skipping the conversion makes it about 2.15 times too short, which is close enough to be one of the choices.
Questions about Dynamics
How do dynamics questions differ from statics ones?
The free-body diagram is the same, with mass times acceleration on the other side of the equation. Most items take one step: constant-acceleration kinematics, Newton's second law, or work and energy. The cost comes from units, above all weight against mass in US customary units.
When should I use energy methods instead of F = ma?
When the question relates speeds to distances, such as a speed after a given travel or an average force over a stopping distance, work and energy skip the time variable entirely. Use F = ma for an acceleration or a force at an instant, and impulse and momentum when time or a collision is involved.
Do I need to memorise mass moments of inertia?
No. The FE Reference Handbook tabulates them for rods, disks, spheres and other common bodies, with the parallel axis theorem. What you need is to see which axis a table entry is about and when to shift it.
Why is Dynamics worth studying when it carries so few questions?
Because its items are short. A projectile range or a kinetic energy is one equation once the units are right, so each is a question answered well under the average time, and that time goes to the long problems elsewhere.
How many study hours this area is worth · Using the handbook under the clock