Point Mass

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

Click once to mark each step.

A point mass marks by default (i.e. immediately upon creation) and autoadvances the video for easy and fast marking. It is wise to set the video clip first so you don't mark unnecessary video frames. Zoom in for accuracy.

Point masses have visible trails by default. Hide the trails if desired using the trails button on the track control.

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.

2. Setting the Mass

A newly created point mass is given a default mass of 1.0 (arbitrary units). Enter a new mass (m >= 0) in the mass field on the toolbar to change it.

3. Displaying Motion Vectors

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

Note: Some motion vectors, especially accelerations, may be very short. You can artificially "stretch" them by a factor of 2 or 4 by clicking on the stretch vectors button on the track control.

You can change the footprint of a vector by first selecting it, then clicking the footprint button on the toolbar and choosing from the list. The ”big arrow” footprint is particularly useful for large classroom presentations.

4. Analyzing Motion Vectors

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

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.

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.

5. 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.

Tracker always draws momentum and net force vectors with dashed lines to distinguish them from motion vectors (dotted lines) and independent vector tracks (solid lines).

6. Linking Motion Vectors

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.