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Undergraduate Curriculum:
Learning Objectives
MCEN 3043 - Dynamics
1. Kinematics of
Particles
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Describe the distinction between a particle and a
rigid body.
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Define position, velocity, and acceleration of a
particle in rectilinear motion. The concepts of position, distance traveled,
velocity, and speed should be understood, and not confused.
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Write the relationships between position,
velocity, and acceleration of a particle in rectilinear motion, under general
conditions, as a function of time. Solve for two of them, given the third, by
differentiation and/or integration. This requires an understanding of the
appropriate initial conditions in each case.
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Describe the physical interpretation of position,
velocity, and acceleration of a particle.
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Identify and analyze special cases of rectilinear
motion (uniform motion, uniformly accelerated motion).
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Write the relationships between position,
velocity, and acceleration of a particle in curvilinear motion, under general
conditions, as a function of time using vector notation.
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Compute the derivative of a vector function and
compute the components of vector fields in Cartesian, path, polar, and
cylindrical coordinate systems. Use these concepts to analyze problems of
projectile motion in both two-and three-dimensions.
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Describe the concept of relative motion and
compute position, velocity, and acceleration of particles in relative motion
and dependent relative motion.
2. Kinetics of
Particles:
Newton’s
2nd Law
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Define mass and linear momentum and explain the
concept of a Newtonian reference frame.
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Write and explain
Newton’s 2nd Law
of motion.
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Write and explain
Newton’s 2nd Law
of motion, and explain the concept of conservation of momentum.
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Systematically use
Newton’s second law to
analyze the motion of a particle acted upon by forces that are constant, and
explicit functions of time, position, and velocity. Identify the appropriate
initial conditions in each case, and describe physical examples of each case.
This should be done for both rectilinear and curvilinear motion.
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Describe the concept of angular momentum of a
particle, write
Newton’s
2nd law in terms of angular momentum, and describe the principle of
angular momentum.
3. Kinetics of
Particles: Energy and Momentum Methods
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Define and compute the work of a force and the
kinetic energy of a particle. Develop the principle of work and energy.
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Apply the method of work and energy to problems
involving a single body or connected bodies.
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Define conservative forces, potential energy, and
the principle of conservation of energy. Identify mechanical loss mechanisms.
Apply the principle of conservation of energy to problems involving a single
body or connected bodies.
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Define the concept of linear impulse and derive
the principle of impulse and momentum.
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Apply the principle of impulse and momentum to
problems of direct and oblique central impact.
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Select the method of analysis that is best suited
for the solution of a given problem (Newton’s
Law, Work and Energy, Impulse and Momentum) and the combination of these
methods.
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Develop the fundamental dynamics equations and
principles for a system of particles.
4. Two-Dimensional
Rigid-Body Kinematics
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Define the fundamental types of plane motion.
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Derive relations defining the velocity and
acceleration of any particle on a rigid body for translation and rotation
about an axis in two- and three-dimensions.
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Decompose general plane motion into the sum of a
translation and a rotation.
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Define and compute the instantaneous center of
rotation.
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Describe and analyze the plane motion of a
particle relative to a rotating frame. Determine the Coriolis acceleration in
plane motion.
5. Two-Dimensional
Rigid-Body Kinetics
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Solve problems in two-dimensional rigid-body
dynamics, regardless of their kinematic characteristics, by equating the sum
of the forces acting on the rigid body to the vectors ma and Ia. To effect this solution, construct appropriate
free-body diagrams.
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Define the work of a couple and the kinetic
energy of a rigid body.
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Apply the method of work and energy to the plane
motion of a rigid body.
Catalog Description
Dynamic behavior of
particle systems and rigid bodies; 2-D and 3-D kinematics and kinetics; impulse,
momentum, potential and kinetic energy, work and collision. Lectures and
homework assignments involve computer work.
Prerequisites: MCEN
2023 APPM 2350
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