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Angular Momentum

Questions Using Planck's Constant

Part 1 An electron microscope operates with a beam of electrons, each of which has an energy of 20 KeV. Use the uncertainty principle in the form delta(x)delta(p) (greater or equal to) h/2 to find the smallest size that such a device could resolve. Planck's constant is 1.0552 × 10^-34 J · s. Answer in units of pm. Part 2

Determining If the Particle Is in an Eigenstate of Lz

A particle is confined in a cubic bow with edge of length a, with V=0 inside the box. The particle is in its ground state, determine whether or not the particle is in an eigenstate of Lz. I do not know how to do this, eigenstate? Detailed solution needed, please.

Hamiltonian Dynamics in an Engine

The governor for an engine, consists of two balls, each of mass m, attached by light arms to sleeves on a rotating rod. The upper sleeve is fixed to the rod, and the lower one of mass M is free to move up and down. Assume the arms to be massless and the angular velocity w to be costant. Find the Lagrangian and Hamiltonian functi

Hamilton's Equations and Force

1) A particle of mass m moves in a plane, under the influence of a central force that depends only on it's distance from the origin. Write the Hamiltonian and Hamilton's equations. 2) A particle of mass m moves in a force filed whose potential in spherical coordinates is V = -(K cos theta)/ r^2. Obtain the canonical equatio

Determine the Velocity of a Child on a Bicycle

A boy is riding a bicycle. Radius of the wheel is .26m and a constant angular velocity of the wheel is .373 rev/sec. Determine the boys velocity Determine the linear velocity of a point on the top of the tire Determine the linear velocity of a point on the bottom of the tire in contact with the ground.

Calculate the Angular Momentum

A 6 kg particle moves to the right at 4 m/s. Calculate its angular momentum with respect to a point O that is found at distance 2m from the particle at angle of 30 degrees below the x-axis (see file for figure).

Angular Momentum Problem

Angular Momentum. See attached file for full problem description. A 1.5 kg particle moves in the xy plane with velocity = (4.2i - 3.6j)m/s. What is the angular momentum of the particle when its position vector is r = 1.5i + 2.2j m

Modern Physics

Modern Physics. See attached file for full problem description.

Lagrangian equations

See attached file for full problem description. A particle moves in a plane under the influence of a force f = -Ar^(alpha -1) directed toward the origin. choose appropriate generalized coordinates, and let the potential energy be zero at the origin. Find the Lagrangian equations of motion. Is the angular momentum abo

Rewinding an audio-tape

In rewinding an audio- or videotape, why does the tape wind up faster at the end than at the beginning?

Moment of inertia problem

1. The figure skater effect. Figure 1 (see attachment) shows the world-renowned Russian figure skater Alicia Itzolova, celebrated for her remarkably cylindrical figure. As she enters her final spin, she may be modeled as a homogeneous cylinder of radius R, height h, and density _, with outstretched arms. The arms are cylinders a

Comet in a parabolic trajectory

A comet in a parabolic orbit around the sun has a least distance of kR, k < 1. Show that the time during which the comets distance is less than R is: (1/3*pi)[2(1-k)]^1/2 * (1+2k) years I have derived the following expression for t as a function of r: t = the integral from r to ro of [2/m (E - u(r) - l^2/2mr^2)]^-1/2 dr

torque and angular momentum ..

1. If a net torque is applied to an object, that object will experience which of the following? a. constant angular velocity b. an angular acceleration c. a constant moment of inertia d. an increasing moment of inertia. 2. A grinding wheel with moment of inertia of 2.0 kg.m2 is initially at rest. What angular momentum wi

Fundamental Physics

Question #1 A grindstone of radius 4.0m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. A. What is the average angular speed of the grindstone? B. What is the magnitude of the angular acceler

A set of problems on work and energy.

1) Evaluate the work done W= Int (from O to P) F &#61476; dr = Int (from O to P) (Fx dx + Fy dy) by the two-dimensional force F = (x2, 2x, y) along the three paths joining the origin to the point P = (1, 1) and defined as follows: (a) This path goes along the x axis to Q = (1,0) and then straight up to P. (Divide the integral i

Question about Orbital Mechanics Problem

The energy and angular momentum of a particle inside a central potential are given by: E = ½*μ *(dr/dt) + V(r) L = μ* r^2 *(dθ/dt)^2 V(r) = (G*μ*M)/r + L^2/(2*μ*r^2) a) Solve these two equations for dr/dt and dθ/dt and show that: dr/dt = +/- [ 2/(μ*(E - V(r)))]^1/2 dθ/dt =

Concentric Spheres

(See attached file for full problem description) --- 2. A particle of mass m is constrained to move between two concentric, impermeable spheres of radii r = a and r = b. The potential V( r ) = 0 between the spheres (a<r<b), and V(r) = otherwise. Find all of the zero angular momentum (l = 0) normalized energy eigenstates, a

Electron Motion of the Helium ion and H-atom

Consider the helium ion: 4, 2 He+, which has two protons and two neutrons in its nucleus. a. What are the two main differences in the description of the motion of the electron in this ion compared to that in in H-atom. b. Write down the normalized first excited state wave function u_210 for this ion. Define your symbols very

Constant Angular Momentum

Each of the disks in the figure has radius r . Each disk can rotate freely about the axis passing through the center of the disk perpendicular to the plane of the figure, as shown. For which diagrams is the angular momentum constant? In your calculations, use the information provided in the diagrams. (See attached file for full

Conservation of Angular Momentum Problem

A uniform rod of mass m_1 and length L rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass m_2, are mounted so that they can slide along the rod. They are initially held by catches at positions a distance r on each side from the center of the rod, and

Magnitude of Angular Momentum of L Bar

A rigid, uniform bar with mass m and length b rotates about the axis passing through the midpoint of the bar perpendicular to the bar. The linear speed of the end points of the bar is v. What is the magnitude of the angular momentum L of the bar? Express your answer in terms of m, b, v, and appropriate constants.

Consider a measuring tape unwinding from a drum of radius r.

The way in which a body makes contact with the world often imposes a constraint relationship between its possible rotation and translational motion. A ball rolling on a road, a yo-yo unwinding as it falls, and a baseball leaving the pitcher's hand are all examples of constrained rotation and translation. In a similar manner, the

Angular Momentum Measured

A system with is measured to have . (a)What is the probabilty of measuring ? (b) In the state , find , , and . (see attachment for question with figures)

Specific Heat of Diatomic Gas Rotations.

Find the specific heat capacity, for the following: (a) An ideal diatomic gas undergoing rotation with no vibrations (b) An ideal diatomic gas undergoing rotation with radial vibrations. (see question for attachment with figures)