{"id":2430,"date":"2011-05-25T18:12:54","date_gmt":"2011-05-26T01:12:54","guid":{"rendered":""},"modified":"2025-02-12T11:55:20","modified_gmt":"2025-02-12T19:55:20","slug":"2430","status":"publish","type":"post","link":"https:\/\/www.vernier.com\/til\/2430","title":{"rendered":"How do I analyze rotational motion using video analysis?"},"content":{"rendered":"

Using Vernier Video Analysis<\/h3>\n

Vernier Video Analysis includes an option to show marked points using polar coordinates (r<\/em>, \u03b8<\/em>) along with the typical (x<\/em>, y<\/em>) coordinates. To select that option from the video tools, click or tap System<\/strong>, select Origin<\/strong>, then select Polar<\/strong>. In addition to r<\/em> and \u03b8<\/em>, r Velocity<\/em> and \u03b8 Velocity<\/em> are also calculated.<\/p>\n

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Using Logger Pro<\/em><\/h3>\n

Logger Pro<\/em> does not have a polar coordinates option. However, you can add calculated columns that calculate the r<\/em> and \u03b8<\/em> values using the X and Y position data. Below are calculated column expressions you can use:<\/p>\n

    \n
  • r = sqrt(“X”^2+”Y”^2)<\/li>\n
  • \u03b8 = atan2(“Y”,”X”); where \u2212\u03c0 \u2264 \u03b8 < \u03c0 rad*<\/sup><\/strong><\/li>\n
  • r Velocity = derivative(“r”,”Time”)<\/li>\n
  • \u03b8 Velocity =derivative(“\u03b8”,”Time”)<\/li>\n<\/ul>\n

    \n

    *<\/sup><\/strong> The angle calculation in Vernier Video Analysis reports \u03b8<\/em> values between 0 and 2\u03c0 radians. If you want to replicate that in Logger Pro<\/em>, use the expression: atan2(“Y”,”X”) \u2212 2*pi*(0.5*abs(“Y”)\/”Y” \u2212 0.5)<\/strong><\/p>\n

    <\/div>\n

    Using Video Physics<\/h3>\n

    Like Logger Pro<\/em>, Video Physics also does not have polar coordinates. While you cannot do any direct calculations within Video Physics, you can export the data to our Graphical Analysis Pro^<\/sup><\/strong> app where you can create calculated columns like those indicated for Logger Pro<\/i>. The calculated column expressions for Graphical Analysis Pro would be as follows:<\/p>\n

      \n
    • r = sqrt(“X”^2+”Y”^2)<\/li>\n
    • \u03b8 = atan2(“Y”,”X”); where \u2212\u03c0 \u2264 \u03b8 < \u03c0 rad“<\/sup><\/strong><\/li>\n
    • r Velocity = firstDerivative(“r”,”Time”)<\/li>\n
    • \u03b8 Velocity =firstDerivative(“\u03b8”,”Time”)<\/li>\n<\/ul>\n

      ^<\/sup><\/strong> Some functions needed for these calculations are not available in the free version of Graphical Analysis; the Graphical Analysis Pro upgrade is required.
      “<\/sup> The angle calculation for Vernier Video Analysis reports \u03b8<\/em> values between 0 and 2\u03c0 radians. If you want to replicate that in Graphical Analysis Pro, use the expression: atan2(“Y”,”X”) \u2212 6.2832*(0.5*abs(“Y”)\/”Y” \u2212 0.5)<\/strong><\/p>\n

      <\/div>\n

      Rotational Motion Beyond One Revolution<\/h3>\n

      If the rotational motion goes beyond one revolution, the angular velocities give unexpected results due to the angle being constrained between 0 and 2\u03c0 (or \u2212\u03c0 and \u03c0) . This is true for all software. One way to work around that is to create a manual column that relates to the number of complete rotations that have occurred up to that point (e.g., 0, 1, 2, etc.). Then, using a new calculated column, calculate the total angular change of the object. See examples below:<\/p>\n

        \n
      • Vernier Video Analysis<\/strong> or Graphical Analysis Pro<\/strong>\n
          \n
        • Rotation = manual column with values 0, 1, 2, …<\/li>\n
        • Total \u03b8 = “\u03b8” + 6.2832 * “Rotation”<\/li>\n
        • T\u03b8 Velocity = firstDerivative(“Total \u03b8”, “Time”)<\/li>\n<\/ul>\n<\/li>\n
        • Logger Pro<\/em><\/strong>\n
            \n
          • Rotation = manual column with values 0, 1, 2, …<\/li>\n
          • Total \u03b8 = “\u03b8” + 2*pi * “Rotation”<\/li>\n
          • T\u03b8 Velocity = derivative(“Total \u03b8”, “Time”)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n
            <\/div>\n