Point Mass

Point mass track

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.

1. Marking and editing the steps

  1. Manual tracking: shift-click once to mark a step at the mouse position, or shift-enter to mark a step at the exact location of the previous step. The video will auto-advance for easy and fast marking. It is wise to set the video clip properties first so you don't mark unnecessary video frames. Zoom in for accuracy.
  2. Autotracking: point mass tracks can be automatically marked as long as the feature of interest has a consistent shape, size, color and orientation. Please see Autotracker for more information.

Don't skip frames--if you do, velocities and accelerations cannot be determined. If you accidentally skip frames, the Datatable view can help you find them.

Point masses have visible trails by default. Hide or shorten the trails if desired using the trails button on the toolbar.

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.

2. Setting the mass and mass unit

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.

Setting the mass--original Setting the mass--typing Setting the mass--final

3. Calculating velocities and accelerations

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/

Velocity and acceleration algorithms

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..

4. Displaying motion vectors

Toggle the vector visibility for all point masses by clicking the velocity button or acceleration button on the toolbar. The vectors are initially attached to their positions (i.e. the tail of the velocity vector for step n is at the step n position).

Velocities at home positions

Note: Some motion vectors, especially accelerations, may be very short. You can artificially "stretch" them by clicking on the stretch button on the toolbar and selecting a stretch factor from the dropdown menu.

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 set different colors for the velocity and acceleration vectors using the appropriate color item on the track button. Motion vector colors are the same as the position by default.

5. Analyzing motion vectors

Select a vector by clicking near its center to display its components on the toolbar.

Vector component fields

Drag a vector to detach it from its position and move it around. Drop the vector with its tail near its position to reattach--it will snap to the position.

Dropping velocity near position Velocities at home positions

A vector will also snap and attach to the origin when the axes are visible. This is useful for estimating and visualizing its components.

Vector tail at origin

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.

6. Displaying momentum and net force vectors

Click the dynamics button on the toolbar to multiply all velocity and acceleration vectors by their mass. This changes them to momentum and net force vectors, respectively.

7. Linking motion vectors

Linking vectors Vectors linked

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.

Chain of vectors

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.

Dragging a vector chain Broken vector chain