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# Angular Momentum

### The solution to Rotational Motion

A 62.99 kg woman stands at the rim of a horizontal turntable having a moment of inertia of 495 kg·m^2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) a

### Laminar Boundary Layer Flow Problem

Text Book : Viscous Fluid Flow by Tasos C. Papanastasiou Download link for the book http://www.filefactory.com/file/ag2609b/n/Viscous_Fluid_Flow_zip http://www.filefactory.com/file/ag261a0/n/chapter08_pdf Problem (8.1) 8.1. Water approaches an infinitely long and thin plate with uniform velocity. (a) Determine the vel

### Ratational Motion: angular vel, acc, and centripetal force

1. There is an analogy between rotational and translational physical quantities. Identify the rotational term analogous to each of the following linear quantities. In each case, give the symbolic expression for the quantity, as well as its name. I filled in three of the lines as examples. (SEE ATTACHMENT for table to fill in)

### The Hydrogen Atom and the Radial Angular Momentum

Hydrogen atom The radial probability density for an electron is r2R2(r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r2R2(r) for an infinitely thin shell and approximately r* r2avg R2(ravg) for a shell of finite thickness r. The quantity ravg is some average

### Conceptual discussions on mechanics problems

Need help with the following physics problems: 1. About medio-lateral axes, the moment of inertia of a person's upper arm (shoulder-elbow segment) was found to be 0.06 kg.m^2 for rotation about the shoulder joint, and 0.08 kg.m^2 for rotation about the elbow joint. Why are these numbers different? 2. A diver's body, whil

### Inertia Tensor of a Rigid Body

A rigid body consists of six particles, each of mass m, fixed tot he ends of three light rods of length 2a, 2b, and 2c, respectively, the rods being held mutually perpendicular to one another at their midpoints. a) Show that a set of coordinate axes defined by the rods are principal axes, and write down the inertia tensor for

### Sample questions are demonstrated.

1. During the later portion of the swing phase of a walking stride the knee is extended from 35 degrees (initial) to 10 degrees (final) over a time period of 0.1 seconds. What was the angular velocity? 2. If an object achieves an angular acceleration of 12 rad/s2 from a moment (torque) of 300 Nm, what is the object's moment o

### Momentum questions are embedded.

1. If a person pushed on a door with a force of 650 N and a moment arm of 0.75 meters, what would be the moment created? 2. A defensive lineman (mass = 88.5kg) is running at 12 m/s, and a linebacker (mass = 84kg) is running at 13.2 m/s. Determine which player has the greater linear momentum, and by how much. 3. The moment

### The spinning motion of a symmetric top

A symmetric top started spinning about a vertical axis. In order not to topple over it must be spinning sufficiently fast. How fast is sufficiently fast? Provide representative sketches for the effective potential for teh case of stable and non-stable motion. When the top is not spinning fast enough to remain spinning in the ver

### Physical quantities of system of particles

The time dependent position of three particles with masses m1=1kg m2=2kg and m3=3kg are: r1 = (3+2t^2)i + 4j r2 = (-2+1/t)i +2tj r3 = i-3t^j Find the total kinetic energy of the system The rotational kinetic energy The total angular momentum The angular momentum of spin The total torque

### Rotational motion: Rate of precession of a rotating wheel.

A wheel with mass less spokes has mass 1 kg and radius 10 cm and is mounted on one end of a mass less axle as figure. The axle rests on a pivot at a point 16 cm from the mounting point and 10 cm from the wheel. At the other end, a mass of 0.8 kg is attached. The wheel spins at an angular frequency of 10 rad/s. What is the

### phonons and lattice vibrations

What is meant by the terms: (i) normal mode and (ii) phonon. Explain why phonons obey Planck-Bose/Einstein statistics. What is the difference between an acoustic mode, and optic mode? Quantized lattice vibrations are called phonons. When a phonon propagetes to a crystal lattice the atomic oscillators excited and vibrate as pe

### A particle of mass m is attached to the end of a light string of length l. The other end of the string is passed through a small hole and is slowly pulled through it. Gravity is negligible. The particle is originally spinning the round the hole with angular velocity w. Find the angular velocity when the string length has been reduced to 1/2 l. Find also the tension in the string when its length is r, and verify that the increase in kinetic energy is equal to the work done by the force pulling the string through the hole.

A particle of mass m is attached to the end of a light string of length l. The other end of the string is passed through a small hole and is slowly pulled through it. Gravity is negligible. The particle is originally spinning the round the hole with angular velocity w. Find the angular velocity when the string length has been re

### the force correponding to the potential energy function

Please see the attached file. 5. Evaluate the force correponding to the potential energy function V(r) = cz/r^3, where c is a constant. Write your answers in vector notation, and also in spherical polars, and verify that is satisfies curl F = 0.

### Angular Momentum Quantum Numbers

Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron.

### Rotational Inertia of a Turntable

A turntable has rotational inertia 0.021 kg-m^2 and is rotating at 0.29 rad/s about a friction-less vertical axis. A wad of clay is tossed onto the turntable and sticks 15cm from the rotation axis. The clay hits with horizontal velocity component 1.3 m/s, at right angles to the turntable's radius, and in a direction that opposes

### Hydrogen Atom: Line Spectra and the Bohr Model

A singly ionized helium atom (He+) has only one electron in orbit about the nucleus. What is the radius of the ion when it is in the n = 3 excited state? I have an idea of how to do the problem, but that is with hydrogen. Please help and thank you very much!

### Principle of Conservation of Momentum

Please see the attachment. 11. A 3.0-kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of 2 m/s. After the collision, the 3.0-kg cart is moving to the left with a speed of 1 m/s. What is the final velocity of the 5.0-kg cart? (a

### Do only part (d): Measuring Angular momentum A particle is in the state with wave function shi = 1/sqrt(2)[Y11 + Y1-1] (a) What value is obtained if L^2 is measured? (b) Does the particle have a definite value of Lz? (c) What are the probabilities of getting results h bar and - h bar and 0 for Lz? Are any other Lz results possible (d) Calculate <shi/Lz/shi> (e) Suppose that when Lz is measured the result h bar obtained. What is the wave function afterwards?

Measuring Angular momentum A particle is in the state with wave function shi = 1/sqrt(2)[Y11 + Y1-1] (a) What value is obtained if L^2 is measured? (b) Does the particle have a definite value of Lz? (c) What are the probabilities of getting results h bar and - h bar and 0 for Lz? Are any other Lz results possible

### Tilted Gyroscope

A gyroscope consists of a flywheel of mass m, which has a moment of inertia I for rotation about its axis. It is mounted on a rod of negligible mass, which is supported at one end by a frictionless pivot attached to a vertical post, as shown in the diagram. The distance between the center of the wheel and the pivot is d. The whe

### Rotation and Angular Momentum

See attachment please. Need FBD for each case. The 0.2 kg ball ( ball is sliding not rotating) and the supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angular velocity of W = 4 radians/sec. The green ball is held in position b = .3 m by the tension T in the yellow cord. If b

### Inverted Pendulum with Counterweights - Equations of Motion

Could someone help me to derive the equations of motions for the system shown in the attach file. Basically it's a 2-dimensional "box" which should be stabilized on its rotating(pin) joint by adjusting counterweights m1 and m2 with linear motors. Counterweights m1 and m2 can move of speed v1 and v2 respectively. We can assume th

### angular velocity of the disk after a ring of sand dropped

A solid disk rotates in the horizontal plane at an angular velocity of 0.067 rad/s with respect to the axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.10 kg*m^2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of

### 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.

### 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

### 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

### 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