Share
Explore BrainMass

Angular Momentum

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

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

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

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 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

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

Rotational Motion: Torque, angular acceleration, velocity

A 3.50 kg counterweight is attached to a light cord, which is wound around a spool . The spool is a uniform solid cylinder of radius 8.00 cm and mass 1.40 kg. (a) What is the net torque on the system about the point O? (b) When the counterweight has a speed v, the pulley has an angular speed w= v/R. Determine the total a

Miscellaneous physics question

1. Competitive divers pull their limbs in a curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocity. What is the effect of these actions on their angular momentum? 2. What is the final velocity

Tension, Force, Momentum, Velocity, Temperature, Energy

1. A 9kg hanging weight is connected to a string over a pulley to a 5kg block that is sliding on a flat table. If the coefficient of kinetic friction is 0.15, find the tension in the string. 2. A 50kg ice skater is moving at 5m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then mo

Rotational Dynamics Simple Harmonic Motion

A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 1.30 rad/s. Friction is negligible. Her arms are outstretched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and dumbbells) is 6.66 kg·m2. By

Calculating velocity and angular velocity

Please help with the following problem. Provide step by step calculations fo reach. A uniform cylinder (A) has a mass ( m = 3 kg ), radius ( r = 150 mm ), and can roll without sliding on a cart ( C ) of mass ( M = 5 kg ). Cylinder (A) is attached to a spring (AB) of stiffness (constant) k = 100 N/m as shown (attached). The s

Angular Velocity and Distance Problems

A 1.62 oz golf ball with a 1.70 in. diameter is hit by a club at point P. Velocity magnitude of the ball's center of mass is 180 ft/s after the impact. What is the angular velocity of the ball? (h = 0.2 in.) A 1 oz. bullet with a horizontal velocity of 350 ft/s strikes a circular disk. The bullet is embedded into the disk aft

Rotation of a Diver

A diver can change her rate of rotation in the air by "tucking" her head in and bending her knees. Lets assume that when she is stretched out straight she is rotating at 1 revolution per second. Now she goes into the "bend and tuck", effectively shortening the length of her body in half. What will her roation be now? a. 5Hz

Running on circular platform

Suppose a 60kg person stands at the edge of a 6.0m diameter circular platform, which is mounted on frictionless bearings and has a moment of inertia of 1800kgm^2. The platform and runner are initially at rest. Calculate the angular velocity of the platform if the runner begins to run 4.2m/s.

Rotating a Professor on a Turntable

Hi I need you help for two questions. 1. A professor steps onto a stationary turntable while holding a rotating bicycle wheel that is rotating with an angular velocity of 15 rad/s pointing upward. The wheels axis of rotation goes through the axis of the turntable. The rotational inertia of the wheel is 1.5 kg m^2 and the co

Mechanics: Dynamics (Translational and rotational motion).

1. Two equal weights of mass M each are connected by a cord passing over a frictionless pulley of mass mp and radius r. An additional weight of mass m is placed on one of the weights of mass M. Derive the expression for: a) system acceleration a; b) cord tensions. 2. A helicopter rotor blade can be considered a long thin

Magnitude of Angular Momentum

1. A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg.m^2/s) relative to the center of the racetrack? 2. A Body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x=5 sin

Angular momentum of a space station

A space station is constructed in the shape of a hollow ring of mass 5.00 x 10^4 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius of 100m. At rest when constructed, the ring is set rotating around its axis so that the people inside experience an effectiv

Angular momentum of a rotating rigid object

A uniform solid sphere of radius 0.500 m and mass of 15.0kg turns counterclockwise about a vertical axis through its center. Find its vector angular momentum when its angular speed is 3.00 rad/s. I think I have worked this problem correctly. (See attachment) Please check my answer and confirm if in correct please point ou

Mechanics, rotation, angular deceleration. Part 3

A flywheel initially rotating at a speed of 800 rev/min, is brought to rest with uniform angular deceleration in 6’s c. At what time will both the radial and tangential components of acceleration be equal in magnitude?