Java applet illustrating motion under the influence of a central force -- the classic problem of a mass moving on a table, connected by a string to another, vertically hanging mass.
Type of Material:
Java applet
Technical Requirements:
Works well with IE 5.5 and Netscape Navigator 4.75
Identify Major Learning Goals:
To allow students to explore aspects of conservation of angular momentum and central forces.
Target Student Population:
Intermediate and possibly Lower Level Undergraduate
Prerequisite Knowledge or Skills:
Kinematics of circular motion; centripetal force; angular momentum of a point mass
Content Quality
Rating:
Strengths:
Nice simulation of a classic problem of undergraduate mechanics. The applet demonstrates both circular motion and stable motion with radial oscillations under the influence of a central force.
Concerns:
Certain initial conditions produce unphysical results. The applet just seems to solve a set of equations without taking into account that there are physical restrictions to some of the parameters. For example, when the radial coordinate becomes larger than the length of the string, the hanging mass rises straight above the table and the string becomes longer and longer. The lack of units is a problem, particularly for lower level students. The theory presented is inadequate for intermediate level students; mv^2/r is not the only relevant term when r is changing.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Recommended Use for Material: Lecture/Demo
Several features of this classical problem can be easily observed and examined from a qualitative perspective.When paused, the user can easily read numerical values for time, radial distance, speed, and angular speed. Students therefore can make measurements, construct data tables and analyze the motion.
Concerns:
Use Material is not Suited For: Stand-alone introduction to motion under the influence of a central force
The lack of units and the inability to separately set speed and radius, makes the simulation more difficult to understand than necessary for lower level students. The units used in the applet are consistent with SI units, but all the numerical values, except for t, are given without units. The red ball has m=1.
Though possible, quantitative analysis is difficult because of the lack of information about the direction of the vectors, and the inability to step through the motion to determine maximum and minimum points. More complete theory would be helpful for intermediate students. The default behavior of changing the hanging mass to maintain circular motion when r or v is changed is counter-intuitive,
and should be changed. The visual clue of enlarging the black dot is insufficient (and possibly confusing).
There are also some problems with the font and subscripts. Fg denotes the gravitational force, but here g represents a subscript. Mg is the mass times the gravitational acceleration. Fg = Mg is not a good way to typeset this equation. Although there is a fair amount of text accompanying the applet, it is not organized effectively, with applet instructions intermixed with physics.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet allows the user to explore circular motion as well as stable radial oscillations. It gives visual as well as numerical information, so data tables can be constructed and data can be analyzed. Viewing direction is easily changed. It features a nice use of left and right buttons to control the applet and to examine two different cases when the radius is changed. There is also the ability to pause the motion, and optionally show the trajectory. The radius and speed of the red ball are easily changed by clicking and dragging.
Concerns:
The lack of frames or separate windows for instructions and the applet makes it awkward to move between the two. The fact that v can be changed by clicking and dragging on the red ball is undocumented, and the effect on the mass of the black ball is confusing. Until fixed, students should be warned about the unphysical situations that follow certain user inputs.
Creative Commons:
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