Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards

Qualitative Aspects of Rotational Dynamics

Rotational Kinematics

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.

Further Description:

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.

Concepts Needed:

Grade 9

Rotation (in revolutions), angular speed (in revolutions/sec), frequency (in revolutions/sec), period (time per revolution)

Grade 10

Frequency f in Hz, period, t or T as reciprocal of f

Grade 11

Axis of rotation, radian as measure of angular displacement, q, s/r, angular velocity, w, as v/r

Grade 12

Angular acceleration, a; frequency f or n (as w/2p);

Empirical Laws or Observed Relationships:

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.

Theories or Models:

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.

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Micro-Unit Description:

Qualitative Aspects of Rotational Dynamics
Students should observe that a force at right angles to a moment arm tends to produce rotation. Since they will not yet understand rotational inertia, they can at best offer their own hypotheses for this phenomenon. They should observe the phenomenon of conservation of angular momentum in situations like the ice skater who brings arms in close or moves them outward.There are several other phenomena associated with rotational dynamics, phenomena observed using tops and bicycles, that allow qualitative understandings of important aspects of rotational dynamics before the introduction of quantitative material in later grades. (b) Rotational inertia can be introduced as the tendency to resist changes in rotational motion but should not be developed further at this grade level.

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