using System; using L=Science.Physics.GeneralPhysics; namespace Serway.Chapter10 { /// /// Example02: CD Player /// On a compact disc (Figure 10.6), audio information is /// stored in a series of pits and flat area on the surface /// of the disc. The information is stored digitally, and /// the alternations between pits and flat areas on the /// surface represent binary ones and zeroes to be read by /// the compact disc player and detected by a system /// consisting of a laser and lenses. The length of a string /// of ones and zeroes representing one piece of information /// is near the center of the disc or near its outer edge. /// In orther that this length of ones and zeroes always passes /// by the laser lens system in the same time period , /// the tangential speed of the disc surface at the location /// of the lens must be constant. This requires, according /// to Equation 10.10, that the angular speed vary as the laser /// lens system moves radially along the disc player, /// the constant speed of the surface at the point of the laser /// len system is 1.3 m/s. /// (A) Find the angular speed of the disc in revolutions /// per minute when information is being read from the /// innermost first track (r = 23 mm) and the outermost final /// track (r = 58mm) /// \omega_i = 5.4 \times 10^2 rev/min /// \omega_f = 2.1 \times 10^2 rev/min /// (B) The maximum playing time of a standard music CD /// is 74 min and 33 s. How many revolutions does the disc /// make during that time? /// \Delta \theta = 2.8 times 10^4 rev /// (C) What total length of track moves past the objective /// lens during this time? /// x_f = 5.8 \times 10^3 m /// (D) What is the angular acceleration of the CD over /// the 4473 s time interval? Assume that is constant. /// \alpha = -7.8 \times 10^{-3} rad/s^2 /// public class Example02 { public Example02() { } private string result; public string Result { get{return result;} } public void Compute() { L.Velocity v = new L.Velocity(); v.Y = 1.3; L.Length inner = new L.Length(); inner.m = 23.0*0.001; L.Length outer = new L.Length(); outer.m = 58.0*0.001; L.AngularVelocity omegain = new L.AngularVelocity(); omegain.Z = v.Y/inner.m; L.AngularVelocity omegaout = new L.AngularVelocity(); omegaout.Z = v.Y/outer.m; //(A) result+=Convert.ToString( omegain.Z*60.0/2.0/Math.PI)+"\r\n"; result+=Convert.ToString( omegaout.Z*60.0/2.0/Math.PI)+"\r\n"; //(B) result+=Convert.ToString( (omegain.Z+omegaout.Z)/2.0*60.0/2.0/Math.PI *(74.0+33.0/60.0))+"\r\n"; //(C) result+=Convert.ToString(v.Y*(74.0*60.0+33.0))+"\r\n"; //(D) L.Time t = new L.Time(); t.s = 4473.0; L.AngularAcceleration alpha = new L.AngularAcceleration(omegaout,omegain,t); result+=alpha.ToString(); } } } /* 539.742850485558 214.03595795117 28097.105084479 5814.9 0 +/- 0 i +0 +/- 0 j -0.00762529533355388 +/- 0 k (rad/s^2) */