Scope, Sequence, and Coordination
A Framework for High School Science Education
Based on the National Science Education Standards
Qualitative Aspects of Rotational Dynamics
The rotational motion of ideal rigid objects can be described using angle of rotation in radians, angular speed, and angular acceleration. Methods of use and analysis are mathematical analogs to translational kinematics, so that many of the same methods are applicable.
Exploring the rotational motion of rigid objects begins with reviewing the motion of a point object moving in a circular path of radius r. The basic concepts of angular "distance," angular speed, and angular acceleration can be developed for this simple model.
Next we can consider ideal rigid bodies of extended size, probably symmetrical in shape like rotating cylinders, and for simplicity we should consider only those cases where there is rotation about an axis of symmetry. The fixed axis of rotation is then defined, and we can introduce the direction of angular displacement as a vector.
The angular velocity is also a vector. This vector character is introduced mainly because the components of angular momentum vectors are used for electron revolution (angular momentum quantum number) and rotation (spin quantum number) in quantum chemistry. Angular accelerations can then be considered.
The kinematics of angular motion of rigid objects is often an analog of the translational motion case and therefore can be easily considered. The angular motion of solid objects about a simply determined axis fixed in space could lead to consideration of motion of nonsymmetrical objects about some axis, particularly in qualitative discussions.
Rotation (in revolutions), angular speed (in revolutions/sec), frequency (in revolutions/sec), period (time per revolution)
Frequency f in Hz, period, t or T as reciprocal of f
Axis of rotation, radian as measure of angular displacement, q, s/r, angular velocity, w, as v/r
Angular acceleration, a; frequency f or n (as w/2p);
AArea@ under an angular speed vs. time curve gives angular displacement. Slope of angular displacement vs. time curve gives angular velocity. Slope of angular velocity vs. time curve gives angular acceleration.
The model of an extended rigid object must be considered from the standpoint of the axis of rotation and the reference lines needed to measure angular motion.