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
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
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
1) Evaluate the work done W= Int (from O to P) F  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
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 =
See attached file
(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
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
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
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
A set of problems on circular and rotational motion, centre of mass, moment of inertia, simple harmonic motion.
1. A bicycle travels 141 m along a circular track of radius 15 m. What is the angular displacement in radians of the bicycle from its starting position? a. 1.0 rad b. 1.5 rad c. 3.0 rad d. 4.7 rad e. 9.4 rad 2. Which equation is valid only when the angular measure is expressed in radians? See the attachment 3.
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
Could some please give detailed solutions to the following past paper Question 3. Please highlight where standard formulas (showing the formulas in bold) are used and make all methods clear explaining what has been done and why. See the attached file.
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
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
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.
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/
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
A solid cube of side 2a and mass M is sliding on a frictionless surface with uniform velocity v as in figure (a) (in attached file). It hits a small obstacle at the end of the table, which causes the cube to tilt as in figure (b) (in attached file). Find the minimum value of v such that the cube falls off the table. Note that th
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
A fireman clings to a vertical ladder and directs the nozzle of a hose horizontally toward a burning building. The rate of water flow is 6.37 kg/s, and the nozzle speed is 12.8 m/s. The hose passes vertically between the fireman's feet, which are 1.30 m below the nozzle. Choose the origin to be inside the hose between the firema
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
I have answers for (a) and (b) but (c) is eluding me! Please shed some light on this supposedly simple problem concerning an object rolling down a slope! See attached file for full problem description.
A sphere of radius mass M and moment of inertia I rolls down a slope that is inclined at an angle phi to the horizontal. The sphere starts from rest and rolls without slipping a distance L down the slope. Choose coordinates x and theta as shown. a) Write down a relationship between x and theta. Please see the attached fi
A sphere of radius mass M and moment of inertia I rolls down a slope that is inclined at an angle phi to the horizontal. The sphere starts from rest and rolls without slipping a distance L down the slope. Choose coordinates x and theta as shown. a) Write down a relationship between x and theta. (Answer x =R*theta) b) Wri
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
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
Please assist me with the attached quantum mechanics questions. Direct sum space, total angular momentum, eigenvectors, scalar operator,
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
A star rotates about its axis through a diameter once in 50 days. At the end of its life, the star collapses to one-hundreth of its original diameter. The rate of rotation of the collapsed star will be: a. 0.02 rotaions per day b. 20 rotaions per day c. 2 rotaions per day d. 200 roations per day