On Mon, Dec 01, 2003 at 04:19:23PM -0600, Chris Schumann wrote: > You may not be, but there should be quite a few on the list. Let's do > some math! Alas, I must pick some nits. > Audio CD's start at 500 RPM and slow down to 200 RPM. That's 1x. > The fast drives go CAV at one speed, and are fastest at the end of > a disc, so let's go with 52x200 or 10,400 RPM. Hopefully your numbers are right here - I didn't check. > The speed of the edge of a disc v=wr which is the rotational > speed times the radius, or 10400RPM * 6cm or 62400cm/min or > (uhm... times 1min/60s times 1m/100cm) 10.4m/s (!) or > 62400 cm/min (times 60min/1hr times 1mi/160934cm) = 23.26 mph. w in v=wr is angular frequency, which is radians per second. "Regular" frequency is w/(2 pi). Or v = 2 pi f r. So the actual speed at the edge is 392000 cm/min = 65.3 m/s = 146 mph. > CD's have a mass of about 20g. A 1g chunk at 10.4m/s should > have 1/2 * m * v * v energy or about 1/20 (need help with unit > here...) joule? Or the same energy as a kilogram dropped from > a height of 5.5mm. (U = mgh) A 1 gram chunk at 65.3 m/s would have 2.1 joules of energy. While the disk is spinning, its kinetic energy = 1/2 I w^2. I, the moment of inertia is 1/2 m r^2. So, KE_rot = 1/2 (1/2 m r^2) (v/r)^2 = 1/4 m v^2 = 16 J , with a CD mass of 15 grams. For comparison, this is the same as the kinetic energy of a golf ball going 59 mph (26 m/s) - which would be slow for a golf ball. Sorry for the abundance of details. -- Jim Crumley |Twin Cities Linux Users Group Mailing List (TCLUG) crumley at fields.space.umn.edu |Minneapolis/St. Paul, Minnesota Ruthless Debian Zealot |http://www.mn-linux.org/ Never laugh at live dragons |Dmitry's free,Jon's next? http://faircopyright.org _______________________________________________ TCLUG Mailing List - Minneapolis/St. Paul, Minnesota http://www.mn-linux.org tclug-list at mn-linux.org https://mailman.real-time.com/mailman/listinfo/tclug-list