Dynamics (EML3013)

Course Description

Dynamics is the first part of an integrated sequence in dynamics, vibrations, and controls. Material includes kinematics and kinetics of particles and rigid bodies, and energy and momentum methods.

Within the SCNS taxonomy, EML is the Mechanical Engineering prefix. The FAMU-FSU College of Engineering publishes this at 3 credits, prerequisites EML3002L and EML3004, giving approximately 45 contact hours at the standard university lecture ratio. It appears at approximately two Florida institutions under this number; most Florida programmes teach the same subject under EGN2322 or EGN3321.

The phrase "first part of an integrated sequence in dynamics, vibrations, and controls" is worth noticing: this course is deliberately positioned as the foundation of the systems side of mechanical engineering, and it feeds directly into EML3014C System Dynamics and Vibrations. Students who treat it as a self-contained hurdle rather than the first term of a three-part idea find the follow-on courses considerably harder.

Dynamics is widely regarded as the hardest course in the engineering mechanics sequence, and the reason is specific: statics has one method, and dynamics has several that are all correct. Knowing which to use is the skill.

Learning Outcomes

Required Outcomes

• Describe position, velocity, and acceleration as vector quantities and relate them by differentiation.
• Analyze rectilinear motion, including motion with variable acceleration.
• Analyze curvilinear motion in rectangular, normal-tangential, and polar coordinates.
• Select an appropriate coordinate system for a given motion.
• Analyze dependent motion of connected particles.
• Analyze relative motion using translating reference frames.
• Apply Newton's second law to particles and construct kinetic diagrams.
• Analyze particle motion under central force and gravitational attraction.
• Apply the principle of work and energy to particles.
• Apply conservation of energy with conservative force systems.
• Calculate power and efficiency in mechanical systems.
• Apply the principle of impulse and momentum to particles.
• Apply conservation of linear momentum and analyze impact.
• Apply the coefficient of restitution to direct and oblique impact.
• Apply angular impulse and momentum to particles.
• Describe planar rigid body kinematics: translation, rotation, and general plane motion.
• Apply relative velocity and relative acceleration equations to rigid bodies.
• Locate and use the instantaneous centre of zero velocity.
• Apply rotating reference frames and account for Coriolis acceleration.
• Calculate mass moments of inertia and apply the parallel-axis theorem.
• Apply the equations of motion to rigid bodies in translation, rotation, and general plane motion.
• Apply work-energy methods to rigid bodies.
• Apply impulse-momentum methods to rigid bodies, including eccentric impact.
• Select the most efficient solution method for a given problem.

Optional Outcomes

• Introduce three-dimensional rigid body dynamics.
• Introduce single-degree-of-freedom vibration.
• Describe gyroscopic motion.
• Use computational tools to simulate dynamic systems.
• Describe Lagrangian formulation at an introductory level.
• Relate content to the FE examination specification.

Major Topics

Required Topics

• Position, velocity, and acceleration
• Rectilinear motion
• Curvilinear motion in multiple coordinate systems
• Coordinate system selection
• Dependent motion
• Relative motion, translating frames
• Newton's second law; kinetic diagrams
• Central force motion
• Work and energy for particles
• Conservation of energy
• Power and efficiency
• Impulse and momentum for particles
• Impact and coefficient of restitution
• Angular impulse and momentum
• Rigid body kinematics in plane motion
• Relative velocity and acceleration
• Instantaneous centre of zero velocity
• Rotating frames and Coriolis acceleration
• Mass moment of inertia
• Rigid body equations of motion
• Work-energy for rigid bodies
• Impulse-momentum for rigid bodies
• Method selection

Optional Topics

• Three-dimensional dynamics
• Introduction to vibration
• Gyroscopic motion
• Computational simulation
• Introductory Lagrangian methods
• FE examination alignment

Resources & Tools

• Engineering Mechanics: Dynamics (R. C. Hibbeler) — the dominant text; the problem sets are the course.
• Vector Mechanics for Engineers: Dynamics (Beer, Johnston, Cornwell) — the other standard.
• Engineering Mechanics: Dynamics (Meriam, Kraige & Bolton) — rigorous and well regarded.
• Schaum's Outline of Engineering Mechanics: Dynamics — inexpensive and problem-dense.
• NCEES FE Reference Handbook — free; the dynamics section is directly examined.
• MIT OpenCourseWare 2.003 — free, and strong on the modelling perspective this course's sequence is building toward.
• MATLAB, Python, or GNU Octave — free in the Python and Octave cases; numerically integrating an equation of motion and plotting the result builds intuition that hand solutions do not.
• A calculator you know thoroughly — and check NCEES's approved calculator list early.
• The Efficient Engineer and Jeff Hanson on YouTube — free, and unusually clear on rigid-body kinematics, which is the part students find hardest.
• A study group — dynamics rewards discussing method selection out loud more than almost any other course.

Career Pathways

• Mechanical engineer — SOC 17-2141; dynamics underlies machinery, mechanisms, and anything that moves.
• Aerospace engineer — SOC 17-2011; flight dynamics, orbital mechanics, and launch vehicle behaviour are this course extended. Florida's Space Coast makes this an unusually direct local pathway.
• Controls engineer — the sequence this course begins leads there; see this repository's EML3014C guide.
• Robotics engineer — manipulator kinematics and dynamics are the core of the discipline.
• Automotive and vehicle dynamics engineer.
• Machine design engineer — cams, linkages, and mechanisms.
• Vibration and noise engineer — a specialization with strong demand.
• Simulation and multibody dynamics analyst.
• Biomechanics — gait and human motion analysis apply the same methods.
• Graduate study in dynamics, controls, or aerospace.
• Licensed professional engineer — dynamics is examined on the FE Mechanical.

Special Information

⚠ Method selection is the actual skill — three approaches, all correct

• Dynamics differs from statics in offering several valid routes to the same answer, and choosing badly turns a five-minute problem into a forty-minute one.
• Newton's second law gives you acceleration at an instant, and it is the right choice when you need forces or when acceleration is the unknown. It requires a free-body diagram and a kinetic diagram, and it is the most general method.
• Work and energy relates positions and speeds without time, and it is the right choice when the question involves distance and velocity and does not ask about time or force. It is a scalar method, which is why it is usually the fastest.
• Impulse and momentum relates velocities across a time interval, and it is the right choice for impact, for short-duration forces, and for anything where momentum is conserved.
• Read the question for what is given and asked. Distance and speed with no time mentioned points to energy; time and velocity change points to impulse-momentum; a demand for a force at an instant points to Newton.
• Conservation laws simplify enormously when they apply — and knowing exactly when they apply (no non-conservative work; no external impulse in a direction) is the examinable subtlety.
• Do not abandon free-body diagrams. They remain essential, and students who stopped drawing them after statics struggle immediately.
• Practise classifying problems before solving them. Working through a problem set deciding only which method applies — without solving — is an unusually efficient use of study time.

⚠ Rigid-body kinematics is where students actually get stuck

• Particle dynamics feels manageable; rigid-body kinematics is the wall. The difficulty is that a rigid body translates and rotates simultaneously, and every point on it has a different velocity.
• The relative velocity equation is the central tool. The velocity of any point equals the velocity of a reference point plus the rotational contribution — and getting the cross product's direction right is where the errors live.
• The instantaneous centre of zero velocity is a genuine shortcut. Locating it turns a general plane motion problem into a pure rotation problem, and for linkages it frequently collapses the work dramatically. Learn to find it quickly.
• The relative acceleration equation has more terms and less forgiveness. The normal (centripetal) component is the one students omit, and omitting it is the single most common rigid-body error.
• Coriolis acceleration appears whenever a point moves relative to a rotating frame, it is counterintuitive, and it is examinable. If a slider moves along a rotating arm, the Coriolis term is there.
• Mass moment of inertia is not area moment of inertia. Students carry the statics formula across and it is wrong — check your units, and note that the parallel-axis theorem applies in both but with different quantities.
• Draw the mechanism at the instant described. A sketch with the geometry and the known directions marked resolves most confusion before any algebra.
• Verify directions physically. If your answer says a wheel's contact point is moving forward relative to the ground while rolling without slipping, something is wrong.

⚠ This is the first course of a sequence — treat it that way

• The catalog explicitly positions this as the first of dynamics, vibrations, and controls, which is a deliberate curricular choice and a useful signal.
• Vibrations is dynamics with a restoring force. A mass-spring-damper system is a direct application of Newton's second law, and the differential equation you will solve there is set up with the technique you are learning here.
• Controls is vibrations with feedback. The transfer function that dominates a controls course describes the same physical system, expressed differently.
• Learn to write equations of motion cleanly. That single skill — free-body diagram, coordinates, second law, tidy differential equation — is what the entire sequence is built on, and it recurs for a career.
• Do not discard the differential equations. The mathematics from MAP2302 is used directly, and students who treated that course as a hurdle find this one harder than it needs to be.
• Numerical solution is worth learning now. Integrating an equation of motion in Python or MATLAB and plotting the response builds intuition for what the equations mean, and it is what practising engineers do.
• Keep your notes and your textbook. You will return to them in the following two courses and again in design work.

⚠ An honest account of the workload

• The engineering mechanics sequence is where engineering programmes lose students, and the reason is rarely intelligence. It is that the courses demand sustained daily problem-solving and reward nothing else.
• Budget eight to twelve hours a week outside class for a course at this level. Students who treat it like a lecture course to be revised before the exam fail it.
• You cannot cram this material. Problem-solving fluency is built by working many problems over many weeks, and there is no compressed substitute.
• Work problems without the solution visible. Reading a worked example produces the feeling of understanding and none of the ability. Attempt first, check after.
• Do more problems than are assigned. The assigned set is a minimum, and the textbook has hundreds more with answers.
• Draw the diagram every time. Free-body diagrams, section cuts, and control volumes are not preliminaries — they are where the problem is actually solved, and skipping them is the single most common cause of wrong answers.
• Carry units through every step and check that the answer is physically plausible. Dimensional analysis catches most algebra errors for free.
• Form a study group and explain solutions aloud. Explaining exposes the gaps that silent reading conceals.
• Go to office hours in week two, not week ten. These courses are cumulative, and a small early gap becomes an insurmountable late one.
• If you are struggling, the problem is usually the prerequisite. Weak calculus or weak algebra shows up here as an inability to finish problems you set up correctly.

⚠⚠ The EGN / EML numbering divergence — and why the 2000/3000 boundary matters here

• Florida teaches the engineering mechanics sequence under two different prefixes. Many institutions use the general engineering prefix EGN — EGN2312 or EGN3311 for statics, EGN2322 or EGN3321 for dynamics, EGN2332C or EGN3331C for mechanics of materials — while the FAMU-FSU College of Engineering and some others use EML numbers within the mechanical engineering prefix.
• Under SCNS these are different courses. Equivalency does not cross prefixes automatically, and it does not cross a C suffix either. Get any transfer determination in writing before you rely on it.
• The sophomore/junior pairing is the trap. This repository documents the pattern across the EGN prefix: statics appears at both EGN2312 (sophomore) and EGN3311 (junior), dynamics at EGN2322 and EGN3321, mechanics of materials at EGN2332C and EGN3331C. Programmes use one consistently with their own positioning.
• Lower-division credit generally cannot satisfy an upper-division requirement. A student who takes statics at the 2000 level and transfers into a programme that requires it at the 3000 level may be told to repeat it — and the reverse is not a problem, which is why the direction of the mismatch matters.
• This is a live issue for A.A. transfer students. Florida's 2+2 articulation guarantees admission to the State University System with junior standing, but it does not guarantee that a specific lower-division engineering course satisfies a specific upper-division requirement in a limited-access programme.
• Check with the receiving department, not only with admissions. Engineering departments make these determinations, and the answer differs between institutions and sometimes between catalog years.
• Plan the mathematics and physics sequence early. Calculus and calculus-based physics are the real gatekeepers, and taking the engineering-technology variants instead closes the A.B.E.T.-EAC route.

⚠ FE exam and PE licensure — this is the accredited engineering pathway

• This course sits inside an A.B.E.T.-EAC accredited engineering programme, which is the pathway that leads directly to professional licensure. That distinguishes it sharply from engineering technology, where the route to a P.E. is longer and carries additional experience requirements — see this repository's ETG, EET, and ETC guides, which document the asymmetry.
• Florida licenses professional engineers under Chapter 471, Florida Statutes, through the Florida Board of Professional Engineers. The sequence is: A.B.E.T.-EAC accredited degree → Fundamentals of Engineering (FE) examination → qualifying experience → Principles and Practice of Engineering (PE) examination → licensure.
• This subject is directly examined on the FE Mechanical exam. The FE is computer-based, offered year-round through NCEES, and most students sit it in their final year while the material is fresh — pass rates are markedly higher for recent graduates than for people who wait.
• The NCEES FE Reference Handbook is the only reference permitted in the exam, and it is free to download. Use it as your reference now, in this course, so that finding an equation in it is automatic by exam day. Students who first open it a week before the FE lose marks purely on navigation.
• Only a licensed P.E. may offer engineering services to the public in Florida, seal drawings, or use the title in a way that implies licensure. Knowing that boundary is professional literacy.
• Rule 11 applies — verify current requirements with FBPE and NCEES directly rather than relying on any course material, including this guide.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement.

EML3013 is 3 credits and approximately 45 contact hours. Expect problem-based homework, midterms, and a final, with partial credit for correct method — showing the free-body diagram, the coordinate system, and the chosen principle matters even when the arithmetic fails.

This subject also appears widely under EGN2322 and EGN3321, and this repository publishes a guide for EGN3321 Engineering Analysis: Dynamics. Programmes use one numbering consistently with their statics positioning — see the numbering flag above, and confirm which your programme and any receiving institution require.