لكل الفيزيائين ارجوكم ساعدوني في الحل

[Foz.i]

السلام عليكم و رحمة الله وبركاته
لكل اهل الفيزياء ساعدوني في حل هذة الاسئله لان اختباري يوم الاحد ومحتاجه الحل ضروري
A bead slide on a smooth rod which is rotating about one end in a vertical plane with
uniform angular velocity ω. Show that the equation of motion is

m ( d2r / dt2 ) = mrω2 – mg sinωt



Q.2. Using Hamiltons’s approach, describe the motion of a particle of mass m constrained
to move on the surface of a cylinder of radius a and attracted toward the origin by a
force that is proportional to the distance of the particle from origin.



Q.3. Show that the transformation Q = log [ ( 1/q) sinP ], P = q cotP is canonical and hence
Find the generating function F.



Q.4. Suppose the potential in a problem of one dimensional of freedom is linearly
dependent on time, such that the Hamiltonian has the form H = ( p2/2m ) – m A t x,
where A is constant. Solve the problem by means of Hamilton’s principal function,
under the initial conditions t = 0, x = 0 and p = mv0.



Q.5. A meson has a speed 0.8c relative to the ground. Find how far the meson travels
relative to the ground, if its speed remains constant and the time of flight, relative to
the system, in which it is at rest is 2 x 10-8 sec.