Introduction to Elementary Dynamics - - - Click here for Symbolic Solutions

Key Concept: In elementary dynamics you study the motion of particles, bodies, and interconnected bodies in one plane (typically the x-y plane). Included is the characterization of the motion itself,
kinematics, and the relationships between forces and moments acting on a body (or bodies) and the resulting planar motion, kinetics. Whether it's kinematics or kinetics, motion must be referred to a "frame of reference", preferably an inertial frame of reference (fixed frame of reference).

In a Nut Shell: The study of elementary dynamics starts with kinematics with focus on velocity

and acceleration. After that it continues with the study of kinetics which uses kinematics as well.

Dynamics

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Kinematics	Kinetics
Relative Velocity	Euler’s 1^st Law Integrated Form of 1^st Law
Relative Acceleration	Euler’s 2^nd Law Integrated Form of 2^nd Law

Kinematics: Position vector, velocity, and acceleration are vectors having both magnitude and direction. Their values change with time when either the magnitude changes, the direction changes, or both. You must account for all changes when calculating the derivatives of these quantities. The basic principles of calculus still hold when calculating these derivatives.

A more complicated problem in kinematics involves the relative motion of an object with respect to different frames of reference. Frames of reference can translate, can rotate, or do both. i.e. You can view the motion of a train with respect to the road (presumably a fixed frame of reference) or perhaps with respect to you in your car as you are driving on a curved road (translating and rotating frame of reference).

Kinetics: Forces and Couples acting on a rigid body cause translational and rotational acceleration. i.e. the body both translates and rotates. Euler’s 1^st Law governs translational

motion of the body's center of mass whereas Euler’s 2^nd Law governs rotational motion od

the body.

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