A point mass track represents a mass moving as a point-like object. It is the most fundamental model of a moving inertial object. Point masses are the building blocks with which more complex and realistic models of physical systems are constructed in classical physics.
Don't skip frames--if you do, velocities and accelerations cannot be determined at the data gaps. If you do skip frames, the Datatable view can help you find and/or autofill them. See Handling data gaps for more information.
To edit a marked step, select it and drag or use the arrow keys on the keyboard to nudge it one pixel at a time. Very fine control is possible at a high zoom level. You can also enter world coordinates directly in the toolbar fields to assign a known position.
Click the visibility button on the toolbar to display a popup menu with items for controlling the display properties of the positions, velocities and accelerations of ALL point masses in a given tab. To control the visibility of an individual point mass, use the Visible checkbox in its track menu.
Here's what the menu items do:
When steps are skipped during marking it creates gaps in the data where velocities and accelerations cannot be determined. Turning on Autofill can automatically fill these gaps using linear interpolation. To turn on Autofill either (a) press the A key, or (b) check the Autofill box in the Datatable view. Pressing the A key repeatedly toggles autofill on and off.
You can disable Autofill in the preferences dialog (Edit|Preferences, Tracks tab). When disabled, you cannot turn it on.
When Autofill is on, gaps are filled by linear interpolation between marked steps. This is equivalent to assuming the track moves with constant velocity during the gap. Clicking or dragging a marked step at either end of a gap automatically updates the autofilled steps in that gap.
When data gaps are visible in the Datatable view, autofilled steps are drawn with an inner circle to distinguish them from marked steps. The images below show a gap before and after being autofilled.
A newly created point mass is given a default mass of 1.0 mass unit (kg by default). Enter a new mass (m >= 0) in the mass field on the toolbar to change the mass. You can change the mass unit at the same time by including it when entering the new mass. In this example, the mass unit is changed to g (grams) in all mass-dependent fields, table columns and plots. Note: all point masses in a given tab have the same units, you cannot have one in kg and another in g.
Velocities and accelerations are calculated from the position-time data using the Finite Difference algorithm shown below. Subscripts refer to step numbers and dt is the time between steps in seconds. The equations are shown only for the x-components; substitute y for x to obtain y-components.
If steps are skipped when marking a point mass, velocities and accelerations cannot be calculated where the required position data is missing. This means velocities are missing both before and after a missing step, and accelerations are missing for 2 steps before and after the missing step.
If you know the point mass bounces off a surface you may wish to use the Bounce Detection algorithm which smooths velocities and accelerations but also detects sudden changes in velocity. Caution: this works very well for bounces but may produce artifacts with some motion. For more information, see http:gasstationwithoutpumps.wordpress.com/2011/11/08/tracker-video-analysis-tool-fixes/
Note: there are many other finite difference algorithms. Tracker's algorithms define the velocity for a step to be the average velocity over a 2-step interval, and the acceleration to be the second derivative of a parabolic fit over a 4-step interval, with the step at the center. Tracker's acceleration algorithm is less sensitive to position uncertainties than others..
You can change the footprint of a motion vector using the appropriate footprint item on its track button. The ”big arrow” footprint is particularly useful for large classroom presentations. You can also assign different colors to the velocity and acceleration vectors, which by default are the same as the position.
Select a vector by clicking near its center to display its components on the toolbar.
Velocity and acceleration vectors are initially attached to their positions (i.e. the tail of the velocity vector for step n is at the step n position). But you can drag a vector to detach it and move it around. Drop the vector with its tail near its position to reattach--it will snap to the position.
A vector will also snap and attach to the origin when the axes are visible. This is useful for estimating and visualizing its components.
Attach all vectors quickly to the origin or positions with the Tails to Origin or Tails to Position items in the point mass track menu.
Vectors can be linked tip-to-tail to visually determine their vector sum. To link vectors, drag and drop one with its tail near the tip of the other. The dropped vector will snap to the tip when it links. You may continue to link additional vectors in the same way to form a chain.
Note: Tracker makes no attempt to check whether it is mathematically appropriate or physically meaningful to link a given set of vectors--it simply makes it possible.
When you drag the first vector (i.e. the vector with the unlinked tail) in a chain, the chain moves as a unit and the vectors remain linked. When you drag any vector further up the chain, however, it detaches and "breaks" the chain.
The path of a point mass is a straight line from each step to the next. The path length L at a given step is the total distance along the path to that step. To see path lengths in a plot or table, choose the variable "L".