user6007: I was watching a you tube video on cropped sensor and they the author mentioned that for video it does not really matter whether you use cropped sensor or full frame? 
Does the sensor size matter for videography? What could be the physics behind this?
Thanks,
NN

user2836: The video you were watching is simply wrong.  The size of the sensor makes every bit as much difference in video as it does in still photography.  Your depth of field and your light sensitivity are still largely determined by your sensor size.
The only thing that really doesn't apply for video is that diffraction limiting isn't a concern since video is so much lower resolution.  (1080p video is only around a 2MP image.)  This one thing makes crop bodies slightly closer to full frames for video, but still does nothing towards the other advantages that full frame has.

user6010: One difference that wasn’t mentioned in other answers is frame downsampling. With a large sensor you have to downsample the image data read from the sensor to the final frame size – for example 1920✕1080 is just around 2 megapixels, whereas the full sensor output is easily ten times as much with recent full-frame cameras.
The problem with downsampling is that the camera is usually not able to do it fast enough while keeping the quality high, it needs to cut corners. As an example, this is a quote from a review of Sony RX-10, a camera with a small 1" sensor:

One of the big selling points on the Cyber-shot DSC-RX10 is its movie
  mode. You wouldn't know it from looking at the already impressive spec
  sheet, but the way the RX10 creates its videos allows for much greater
  quality than most other cameras.
The reason for the higher quality is how video is sampled. Since the
  sensors on the vast majority of cameras cannot be 'read out' quickly
  enough, they don't read the whole sensor when recording video. Instead
  they skip lines of pixels, which means that the amount of data used to
  generate is frame is reduced. The gaps between these lines reduce the
  resolution they can capture, and can introduce moiré.
The RX10, on the other hand, samples the entire 1"-type sensor, so no
  lines are skipped. The results are noticeable both in our test scene
  and real world samples.

In other words, smaller sensor can under some circumstances mean less downsampling artifacts and higher image quality.

user4089: It depends.
All of the questions at http://photo.stackexchange.com regarding the relationship between sensor size and Depth of Field (DoF) apply to video as well. (See, for example: https://photo.stackexchange.com/q/12098/15871, https://photo.stackexchange.com/questions/7904/how-does-background-blur-bokeh-relate-to-sensor-size, and especially https://photo.stackexchange.com/questions/3986/when-do-the-differences-between-aps-c-and-full-frame-sensors-matter-and-why)   If you want very shallow depth of field a FF will give you shallower DoF for the same subject distance, field of view (FoV), and aperture than a  cropped sensor will. This is because the FF camera must use a longer focal length than the crop sensor to achieve the same FoV from the same subject distance. If you want very large depth of field the cropped sensor will have the advantage over the FF camera with the same distance/FoV/aperture.
I think what the comment you heard might have been addressing was the difference in resolution that once existed between most cropped sensor cameras and most full frame cameras. Just a few years ago most APS-C cameras ranged from about 10-12MP while FF cameras where at around 18-20MP. This is not so much the case any more as improvements in sensor technology have allowed APS-C cameras in the 18-20MP range. Since 1920X1080 HD video is only about 2MP per frame, any camera in the 10MP+ range is going to downsize the output of the sensor to 1920X1080 so there is not much difference between a 12MP APS-C camera and a 20MP full frame camera in that regard.

6007: <p>I was watching a you tube video on cropped sensor and they the author mentioned that for video it does not really matter whether you use cropped sensor or full frame? </p>

<p>Does the sensor size matter for videography? What could be the physics behind this?</p>

<p>Thanks,
NN</p>
 2836: <p>The video you were watching is simply wrong.  The size of the sensor makes every bit as much difference in video as it does in still photography.  Your depth of field and your light sensitivity are still largely determined by your sensor size.</p>

<p>The only thing that really doesn't apply for video is that diffraction limiting isn't a concern since video is so much lower resolution.  (1080p video is only around a 2MP image.)  This one thing makes crop bodies slightly closer to full frames for video, but still does nothing towards the other advantages that full frame has.</p>
 6010: <p>One difference that wasn’t mentioned in other answers is frame downsampling. With a large sensor you have to downsample the image data read from the sensor to the final frame size – for example 1920✕1080 is just around 2 megapixels, whereas the full sensor output is easily ten times as much with recent full-frame cameras.</p>

<p>The problem with downsampling is that the camera is usually not able to do it fast enough while keeping the quality high, it needs to cut corners. As an example, this is a quote from a <a href="http://www.dpreview.com/reviews/sony-cybershot-dsc-rx10/7" rel="nofollow">review of Sony RX-10</a>, a camera with a small 1" sensor:</p>

<blockquote>
  <p>One of the big selling points on the Cyber-shot DSC-RX10 is its movie
  mode. You wouldn't know it from looking at the already impressive spec
  sheet, but the way the RX10 creates its videos allows for much greater
  quality than most other cameras.</p>
  
  <p>The reason for the higher quality is how video is sampled. Since the
  sensors on the vast majority of cameras cannot be 'read out' quickly
  enough, they don't read the whole sensor when recording video. Instead
  they skip lines of pixels, which means that the amount of data used to
  generate is frame is reduced. The gaps between these lines reduce the
  resolution they can capture, and can introduce moiré.</p>
  
  <p>The RX10, on the other hand, samples the entire 1"-type sensor, so no
  lines are skipped. The results are noticeable both in our test scene
  and real world samples.</p>
</blockquote>

<p>In other words, smaller sensor can under some circumstances mean less downsampling artifacts and higher image quality.</p>
 4089: <p>It depends.</p>

<p><strong>All of the questions at <a href="http://photo.stackexchange.com">http://photo.stackexchange.com</a> regarding the relationship between sensor size and Depth of Field (DoF) apply to video as well.</strong> (See, for example: <a href="https://photo.stackexchange.com/q/12098/15871">https://photo.stackexchange.com/q/12098/15871</a>, <a href="https://photo.stackexchange.com/questions/7904/how-does-background-blur-bokeh-relate-to-sensor-size">https://photo.stackexchange.com/questions/7904/how-does-background-blur-bokeh-relate-to-sensor-size</a>, and especially <a href="https://photo.stackexchange.com/questions/3986/when-do-the-differences-between-aps-c-and-full-frame-sensors-matter-and-why">https://photo.stackexchange.com/questions/3986/when-do-the-differences-between-aps-c-and-full-frame-sensors-matter-and-why</a>)   If you want very shallow depth of field a FF will give you shallower DoF for the same subject distance, field of view (FoV), and aperture than a  cropped sensor will. This is because the FF camera must use a longer focal length than the crop sensor to achieve the same FoV from the same subject distance. If you want very large depth of field the cropped sensor will have the advantage over the FF camera with the same distance/FoV/aperture.</p>

<p><strong>I think what the comment you heard might have been addressing was the difference in resolution that once existed between most cropped sensor cameras and most full frame cameras.</strong> Just a few years ago most APS-C cameras ranged from about 10-12MP while FF cameras where at around 18-20MP. This is not so much the case any more as improvements in sensor technology have allowed APS-C cameras in the 18-20MP range. Since 1920X1080 HD video is only about 2MP per frame, any camera in the 10MP+ range is going to downsize the output of the sensor to 1920X1080 so there is not much difference between a 12MP APS-C camera and a 20MP full frame camera in that regard.</p>
