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)
*/