![]() ![]() As a result, the work done by a force can be positive, negative, or zero, depending on whether the force is generally in the direction of the displacement, generally opposite to the displacement, or perpendicular to the displacement. The components of a vector can be positive, negative, or zero, depending on whether the angle between the vector and the component-direction is between 0 ° 0 ° and 90 ° 90 ° or 90 ° 90 ° and 180 ° 180 °, or is equal to 90 ° 90 °. Recall that the magnitude of a force times the cosine of the angle the force makes with a given direction is the component of the force in the given direction. From the properties of vectors, it doesn’t matter if you take the component of the force parallel to the displacement or the component of the displacement parallel to the force-you get the same result either way. In words, you can express Equation 7.1 for the work done by a force acting over a displacement as a product of one component acting parallel to the other component. Which choice is more convenient depends on the situation. In two dimensions, these were the x- and y-components in Cartesian coordinates, or the r- and φ φ-components in polar coordinates in three dimensions, it was just x-, y-, and z-components. We could equally well have expressed the dot product in terms of the various components introduced in Vectors. We choose to express the dot product in terms of the magnitudes of the vectors and the cosine of the angle between them, because the meaning of the dot product for work can be put into words more directly in terms of magnitudes and angles. The infinitesimal work is the dot product of these two vectors the total work is the integral of the dot product along the path. The force acting on a particle and its infinitesimal displacement are shown at one point along the path between A and B. This aspect of iFlicks 2 is without doubt the best part of the whole software.Figure 7.2 Vectors used to define work. And this is an area that iFlicks 2 absolutely excels when compared to the competition – if it’s unsure that it’s found a match, but has various options it thinks it could be, it’ll popup a ‘search’ box which gives you the option to edit the video title and type (ie, movie, tv show) and it will show you a list of the options it’s already found, enabling you to choose the one you want to use. So long as your file is named appropriately there’s no reason it should fail – unless no-one has put the data into the online sources in the first place. iFlicks will automatically attempt to look up the metadata for your video file based on its filename and this is extremely intelligent and has found about 98% of files I’ve thrown at it. Converting the files is as simple as dragging and dropping your chosen files from Finder onto the main window (see right – click the image for a larger, clearer version).
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