Using Vernier Video Analysis

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

Using Logger Pro

Logger Pro does not have a polar coordinates option. However, you can add calculated columns that calculate the r and θ values using the X and Y position data. Below are calculated column expressions you can use:

• r = sqrt(“X”^2+”Y”^2)
• θ = atan2(“Y”,”X”); where −π ≤ θ < π rad^*
• r Velocity = derivative(“r”,”Time”)
• θ Velocity =derivative(“θ”,”Time”)

^* The angle calculation in Vernier Video Analysis reports θ values between 0 and 2π radians. If you want to replicate that in Logger Pro, use the expression: atan2(“Y”,”X”) − 2*pi*(0.5*abs(“Y”)/”Y” − 0.5)

Using Video Physics

Like Logger Pro, 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^{^} app where you can create calculated columns like those indicated for Logger Pro. The calculated column expressions for Graphical Analysis Pro would be as follows:

• r = sqrt(“X”^2+”Y”^2)
• θ = atan2(“Y”,”X”); where −π ≤ θ < π rad^“
• r Velocity = firstDerivative(“r”,”Time”)
• θ Velocity =firstDerivative(“θ”,”Time”)

^{^} Some functions needed for these calculations are not available in the free version of Graphical Analysis; the Graphical Analysis Pro upgrade is required.
^“ The angle calculation for Vernier Video Analysis reports θ values between 0 and 2π radians. If you want to replicate that in Graphical Analysis Pro, use the expression: atan2(“Y”,”X”) − 6.2832*(0.5*abs(“Y”)/”Y” − 0.5)

Rotational Motion Beyond One Revolution

If the rotational motion goes beyond one revolution, the angular velocities give unexpected results due to the angle being constrained between 0 and 2π (or −π and π) . 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:

• Vernier Video Analysis or Graphical Analysis Pro
  • Rotation = manual column with values 0, 1, 2, …
  • Total θ = “θ” + 6.2832 * “Rotation”
  • Tθ Velocity = firstDerivative(“Total θ”, “Time”)
• Logger Pro
  • Rotation = manual column with values 0, 1, 2, …
  • Total θ = “θ” + 2*pi * “Rotation”
  • Tθ Velocity = derivative(“Total θ”, “Time”)

Download Example Files