tag:blogger.com,1999:blog-7148772820652335062.post6270467068233291710..comments2016-10-26T11:12:28.863-04:00Comments on Free/Libre Open Source Science Education: Conservation of Energy ConundrumSteve Dickiehttps://plus.google.com/103412747657062364551noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-7148772820652335062.post-32677503821637532172015-03-04T12:31:04.174-05:002015-03-04T12:31:04.174-05:00The rotational inertia is the same so the rotation...The rotational inertia is the same so the rotational speed will be the same. The difference is, you are rotating about 2 axles with different diameters. Therefore the wheel will with the larger axle will travel the same distance with less rotations. If you watch the video and count the rotations of the “wide one” (smaller diameter) it rotates approximately 10 times and the “narrow one” (lager diameter) rotates 5 times.<br /><br />PE=KE<br />mgh=1/2 mv^2<br />w is omega<br />mgh=1/2 mv^2 + ½ Iw^2<br /><br />w=v/r<br /><br />Therefore:<br />mgh=1/2 mv^2 + ½(v/r)^2<br /><br />mgh=(v^2 / 2) (m+ I/r^2)<br /><br />v = sqrt[(2mgh)/(m+I/r^2)]<br /><br />m, g, h & I are all equal between the 2 runs.<br /><br />The only difference is r (radius of the axle).<br /><br />Robert Dickiehttps://www.blogger.com/profile/13328392946592815531noreply@blogger.comtag:blogger.com,1999:blog-7148772820652335062.post-75201476760891523672015-03-04T06:51:02.517-05:002015-03-04T06:51:02.517-05:00Rotational energy does indeed dominate. Nearly all...Rotational energy does indeed dominate. Nearly all the energy is rotational with very little is translational. Here are my calculations:<br />http://youtu.be/R2fduZy6dUoSteve Dickiehttps://www.blogger.com/profile/08605575656767405786noreply@blogger.comtag:blogger.com,1999:blog-7148772820652335062.post-50615996067773899032015-03-03T09:53:15.162-05:002015-03-03T09:53:15.162-05:00If the moment of inertia is large enough, the rota...If the moment of inertia is large enough, the rotational KE will dominate. That means that the translational speed can change by a lot and not really change the KE much. That will lead to only a very small change of the rotational speed (at a point where you expect the total KE to be the same due to having fallen the same amount).Andy Rundquisthttp://arundquist.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-7148772820652335062.post-72485049655818998792015-03-02T20:02:34.570-05:002015-03-02T20:02:34.570-05:00I'm guessing that rotational energy dominates ...I'm guessing that rotational energy dominates over translational energy, is that true? The narrower rails result in a larger "wheel radius", so through v = omega * R, they lead to higher translational velocity for the same rotation rate.Chris Goeddehttps://www.blogger.com/profile/00183311934944462192noreply@blogger.comtag:blogger.com,1999:blog-7148772820652335062.post-55251879298129783622015-03-02T17:31:17.081-05:002015-03-02T17:31:17.081-05:00I recorded it at 240 fps.I recorded it at 240 fps.Steve Dickiehttps://www.blogger.com/profile/08605575656767405786noreply@blogger.comtag:blogger.com,1999:blog-7148772820652335062.post-82875035891276940392015-03-02T17:27:31.309-05:002015-03-02T17:27:31.309-05:00What was the frame rate of the high speed camera? ...What was the frame rate of the high speed camera? I'm just wondering if it's a strobe artifact vs real.Andy Rundquisthttp://arundquist.wordpress.comnoreply@blogger.com