In this problem we consider rotational motion of a diatomic molecule such as carbon monoxide or...
Consider a rigid heteronuclear diatomic molecule of bond length d rotating in the xy plane about the z-axis. We have seen that the Hamiltonian for this system is H = P2/(2), where y is the reduced mass, and p = ( y) is the relative momentum. Define the angular momentum operator about the z-axis as L. = fpy - yp... a. Show that Ê, Î2] = 0. b. Show, therefore, that the eigenfunctions of A are also eigenfunctions of L....
Please fully answer ALL parts! :-) Thank you so much in advance!! 1) This week, we introduced a new model, the rigid rotor, that can be used to describe rotating molecules. Before we get into problems that describe the quantum properties of a rigid rotor, let's quickly review the classical behavior of a rotating molecule. Consider a single atom with mass m rotating about the origin in a circular orbit with radius r. If the particle's linear momentum is p...
Problem 1 (5 pt.) In the last class, we will consider the gyroscopie motion of a heavy symmetrical top whose lowest point is fixed. The effective potential energy of the top is given by + mgl cos ?, where M, is the constant angular momentum component along the vertical Z axis (fixed), Ms is the constant angular momentum component along the zs axis (the moving axis of symmetry of the top), i is the principal moment of inertia about the...
Please solve only (e), and only if you're certain you're correct. Thank you. Angular momentum and choice of origin: Adding angular momentum to a collision problem often feels confusing or ad hoc. What we're going to do here is verify that adding angular momentum to a collision problem isn't incompatible with anything we've done previously, by considering a very simple collision problem: One particle, moving with a velocity vo, collides with another, sticks with it, and then they move together...
please guys this is one question with 2 parts. A student sits on a freely rotating stool holding two dumbbells, each of mass 3.05 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.07 m from the axis of rotation and the student rotates with an angular speed of 0.740 rad's. The moment of inertia of the student plus stool is 2.57 kg: m2 and is assumed to be constant. The student pulls the...
The tidal forces between the Earth and the Moon slowed down the Moon's rotation about its own axis until the rotation period became equal to the Moon's orbital period around the Earth as we observe today. The same effect is also slowing down the Earth's rotation about its own axis and increasing the separation \(D\) between the Moon and the Earth at a rate of \(\Delta D / \Delta t=3.8 \mathrm{~cm}\) per year. In this problem, you can ignore the...
the question is in last picture. i provided the lab content... I need guidance. thank you. INVESTIGATION 10 ROTATIONAL MOTION OBJECTIVE To determine the moment of inertia I of a heavy composite disk by plotting measured values of torque versus angular acceleration. THEORY Newton's second law states that for translational motion (motion in a straight line) an unbalanced force on an object results in an acceleration which is proportional to the mass of the object. This means that the heavier...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Procedure 1, 2, 3 Mass of a clamp: 21.5 True mass of meter stick: _133.6 g Center of mass of meter stick: _50 cm True weight of unknown mass: _212.99_ Procedure 4 Position of the 100-g mass: 10.0 cm Position of equilibrium: _30.9 cm Mass of the stick from method of torques: Procedure 5 Position of the 100-g mass: 10.0 cm Position of the 200-g mass: _90.0 cm Position of equilibrium of meter stick: Procedure 6 Position of unknown mass...
Matching A. Metric unit of force B. Unit of work in the metric system C. Metric unit of power D. Unit of work in English system E. Unit of pressure in metric system named after the scientist Torricelli F. Mass per unit volume G. The force that is dependent on the masses and distance between them H. A unit of angular measure I. The acceleration of and object traveling with a circular motion J. The displacement of an object as...