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Angular Momentum

Rotational Dynamics

A person is hanging motionless from a vertical rope over a swimming pool. She let it go of the rope and drops straight down. After letting go, is it possible for her to curl into a ball and start spinning? Give a brief justification for your answer.

Spin Angular Monentum

(A)A particle with spin 1 has orbital angular momentum L_lowercase=0. What are the possible values for the total angular momentum Quantum number j? (B)The same particle has L_lowercase=3. What are the possible values for j? I need to know how to do a problem like this, detailed solution please.

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

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

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.

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).

Modern Physics

Modern Physics. See attached file for full problem description.

Rewinding an audio-tape

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

Three problems on moment of inertia.

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 modelled as a homogeneous cylinder of radius R, height h, and density _, with outstretched arms. The arms are cylinders

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

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

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 =

Angular States in Quantum Mechanics

(See attached file for full problem description) --- 3. Let denote the eigenstates of L2 and Lx; i.e. L2 = l(l+1)h-bar2 and Lx = m*h-bar* a. Explain briefly why you can always express any given as a superposition of spherical harmonics Yl'm' with l'=l. b. In particular, for each m = +1,0,-1, find the constants a,

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

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

What is the magnitude of the angular momentum L of the 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

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)

Diatomic gas.

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)

Quantum Number Determination

For principle quantum number n = 6 given for electrons in an atom, how many different values of the following quantities are possible? (*Do not list the identity of the states, just tell how many there are and show any supporting calculations.) a) l b) m (sub l): ml c) m (sub )s: ms d) all possible states for n=6

Angular Speed after a Collision

Please show all work. A solid wood door, 90.0 cm wide by 2 m tall has a mass of 35kg. It is ajar and at rest. A ball with a mass of 500g is thrown perpendicular to the door with a speed of 20m/s and hits the door 60cm from the hinged side. The ball rebounds with a speed of 16 m/s along the same line. What is the angular spe

Calculating common angular speed

Two wheels with rotational inertias of 1.0 kg m^2 and 1.5 kg m^2 are rotating on the same axis at 20 rads and 12 rads respectively, in opposite directions. If the wheels are suddenly coupled together, find the common angular speed of the wheels after being coupled.

Totational Motion: Bullet stricks a hanging rod.

A thin uniform rod of mass 400 g and length 60.0 cm is suspended from a pivot and is free to rotate about it in any direction. A bullet strikes the rod at a distance of 46.0 cm from the pivot and gets stuck in it. The bullet was initially moving at a speed of 300 cm/s and was spinning about its forward-backward axis at 17.0 rad/

Rotational motion: A stationary rod is struck at one end.

A uniform rod is resting along the x-axis on a frictionless table with its center of mass at the origin. It is suddenly struck near one end by a blow in the +y direction. The mass of the rod is M=175 g and the impulse applied by the blow is K=74 g m/s. Immediately after the rod is struck, (a) what is the velocity of the cente