Please show all steps and explanation, ty! Show that in the cylindrical (polar) coordinates (r, ø, z), which are related to the rectangular coor-dinates by x = r cos ø, y = r sin ø, z = z, the z-component of the angular momentum of a particlewith mass m, M, = m(xý – yi), is equal toM, = mr²ó.Then show thatMz = Pø =Tewhere L =(1/2)m(r2 + r²o² + ¿²) – U (r, ø, z) is the Lagrangian for the particle in the cylindricalcoordinates. This exercise shows that the angular momentum is a generalized momentum corre-sponding to an angle regarded as a generalized coordinate.

Answered: Image /qna-images/answer/4ac85189-e6b8-4a0a-812f-ad61c605d835.jpg

Show that in the cylindrical (polar) coordinates (r, 6, z), which are related to the rectangular coor- dinates by x = r cos o, y = r sin o, z = z, the z-component of the angular momentum of a particle with mass m, M, = m(xỷ – yà), is equal to M, = mr²6. Then show that M2 = Pø = те where L = (1/2)m(i2 + r²6² + ¿²) – U(r, ø, z) is the Lagrangian for the particle in the cylindrical coordinates. This exercise shows that the angular momentum is a generalized momentum corre- sponding to an angle regarded as a generalized coordinate.

Show that in the cylindrical (polar) coordinates (r, 6, z), which are related to the rectangular coor- dinates by x = r cos o, y = r sin o, z = z, the z-component of the angular momentum of a particle with mass m, M, = m(xỷ – yà), is equal to M, = mr²6. Then show that M2 = Pø = те where L = (1/2)m(i2 + r²6² + ¿²) – U(r, ø, z) is the Lagrangian for the particle in the cylindrical coordinates. This exercise shows that the angular momentum is a generalized momentum corre- sponding to an angle regarded as a generalized coordinate.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter9: Atomic Structure

Section: Chapter Questions

Problem 2P

See similar textbooks

Similar questions

. Consider a system of N particles in a uniform gravitational field. Prove that the total gravitational torque about center of mass(CM) is zero.?
If the diameter of the moon as seen from earth subtends at an angle of about 0.5% what isthe probability that a laser beam aimed in a random direction from the Earth’s surface will hit the moon?
Answer without rounding off: (COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 2.1 x 106 m through the center of a planet with a radius of 7.7 x 106 m. If the mass of the planet is 46.5 x 1015 kg, measure the displacement of the ball at time t = 6 s?
With what force does a homogeneous ball of mass M attract a material point of mass m, located at distance a from the center of the ball (a>R)?
If Force B on the x-z plane is equal to 300N and h = 4m and v = 10m, then what is the i and k components of Force B?
Why is Moment B and C equal to zero?
Two masses constrained to move in a horizontal plane collide. Given initially m₁ = 85 gms, m₂ = 200 gms; u₁ = 6.48 cms/sec and u₂= - 6.78 cms/sec, find the veloctiy of centre of mass.
Can a particle moving under an inverse square repulsive force trace a closed orbit? Explain in brief.
A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) In what kind of orbit is this particle moving?
Rock A of mass M and another rock B of mass 2M are released from a height h above the ground. Upon impact which relationship correctly states the momenta of rocks A and B?
Consider two particles A and B of masses m and 2m at rest in an inertial frame. Each of them are acted upon by net forces of equal magnitude in the positive x direction for equal amounts of time t. Moment of the particles A and B in centre of mass frame respectively are?