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Kinematics of Particles
General Outcomes: Ability to analyze motions of particles
in different coordinate systems.
Specifics: Dispelling common misconceptions that x=(1/2)at^2,
v=at, etc., are general relations, not just for constant acceleration,
etc., and how/when to integrate general relations. Developing a
feel for path-dependent coordinate systems. Concepts of taking time
derivatives of unit vectors that change direction first appear here
and are needed throughout course. Understanding of elementary relative
velocity and acceleration equations, presented as solutions of vector
triangles by trigonometry, and solutions of the scalar equations
found from equating vector components algebraically. Students take
a long time to become comfortable with the second method, although
it is essential later in the course when geometric methods become
impractical.
Dynamics of Particles
General Outcomes: Ability to set up free body diagrams and
determine resulting motion. Understanding of work-energy and impulse-momentum
principles.
Specifics: Free body diagrams. Knowing how to identify how
many unknown quantities there are in a problem, and that an equal
number of independent equations are required to determine them.
As a corollary, knowing when kinematic relations are required to
supplement the independent equations obtained from Newton's law.
Clearing up misconceptions about centrifugal force. Understanding
when it is more convenient to use work-energy or impulse-momentum
methods rather than to start with Newton's law. Understanding how
to evaluate the work integral along a path, and noting which components
do work and which do not. Understanding of negative work done on
a system, especially friction. Understanding how to evaluate cross
products that arise in angular momentum. Incorporating relative
motion equations in Newton's law, and the significance of an inertial
reference frame, e.g., when can we consider motion on a rotating
frame (earth) to be inertial and subject to direct application of
Newton's law. Conservation of momentum but usually not energy in
impact.
Systems of Particles
Significance of the mass center in the dynamics of systems of particles.
Understanding alternative forms of the angular momentum equations
and reasons for using them.
Plane Kinematics of Rigid Bodies
Understanding how kinematic constraints are used to determine motions
of interrelated components. Appreciation of instantaneous center
of zero velocity. Analysis of motion in rotating reference frames.
Developing more skill in solving vector equations.
Plane Dynamics of Rigid Bodies
Development of physical feel for mass moment of inertia. Basic problem
solving skills: Set up force/moment equations, count unknowns, and
supplement with enough kinematic relations to solve system and predict
motion or determine forces.
3D Motion
Appreciation of how to relate and combine different angular velocity
vectors, and to visualize the resulting motion and understand what
is rotating about what. To be exposed to the inertia tensor and
understand the significance of principal axes. Elementary principles
of gyroscopic motion.
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