Rotational energy Definition and 108 Threads

First, energy of a disk: \int \frac{dm}{2}r^2 \omega^2 =\frac{\omega^2}{2}\int_0^R m\frac{2 \pi r dr}{\pi R^2}r^2 =\frac{m\omega^2}{ R^2}\int_0^R r^3 dr=\frac{m\omega^2 R^2}{4 } Which agrees with other sources. However, in the following lies my problem: The equation for a circle...

Homework Statement So I'm stuck on part (ii) where we have to solve the rotational energy levels. Problem: http://screencast.com/t/9rZStJdG3wJ The answer is ii) 0, 3.84 cm-1, 11.52 cm-1 Homework Equations Equations: http://screencast.com/t/ubFEheGBz The Attempt at a Solution...

Homework Statement Suppose three masses are arranged as shown, connected by a rodless mass. (2 kg)-------(6 kg)--------(4 kg) 2m 3m a) If this object is free to rotate in space, about what point will it spin? Cm = 2(0) + 6(2) + 4(5)...

Hello forum members... I have a problem in calculating the energy of rotational levels. Kindly help me...The question goes like this: A Caroussel(merry-go-round) of diameter 20 m and weight 1 ton( =1000 kg that is evenly distributed on the discs) rotates 10 times per minute. Calculate the...

Homework Statement A string is wrapped several times around the rim of a small hoop with radius 8.00 and mass 0.180 . The free end of the string is held in place and the hoop is released from rest. After the hoop has descended 95.0 , calculate the angular speed and speed of its center...

Homework Statement An object, consisting of two point masses with mass m are connected by a rigid shaft with negligible mass. They are lying horizontally at rest. One of the point masses is instantly given a speed of v. Calculate the total energy of the system once the system has stopped...

Homework Statement A uniform disk with mass m = 9.32 kg and radius R = 1.37 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 340 N at the edge of the disk on the +x-axis, 2) a force 340 N at the edge of the disk on the –y-axis...

Homework Statement A diatomic molecule can be modeled as two point masses, m1 and m2, slightly separated. If the molecule is oriented along the y-axis, it has kinetic energy K when it spins about the x-axis. What will its kinetic energy (in terms of K) be if it spins at the same angular...

Homework Statement A solid steel sphere of radius 10 cm and a mass of 1.5 kg rolls down a 1.25 m incline that makes an angle of 20 degrees with the horizontal. Calculate the linear velocity of the following points relative to the ground, when it reaches the bottom of the incline. a) The...

Hi guys so this is my first time posting a question on this amazing forum, i hope i am doing this right since i read that no one will help me if i am missing something. Anyways, i am dealing with a physics problem that it driving me crazy (mainly because my teacher does not explain anything!)...

How do i convert spring energy to rotational energy? I am building a 'green device' that allows a bicycle to move forward using stored energy (compressed spring energy). So i am figuring out how do i change the spring energy stored to rotational energy so that th bike will be able to propel...

A small, solid, uniform ball is to be shot up from point P so it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance (d=6cm) from the right edge of the plateau. The vertical...

Homework Statement A solid, uniform spherical ball rolls without slipping up a hill. At the top of the hill it is moving horizontally, and then it goes over a vertical cliff. How far from the foot of the cliff does the ball land, and how fast is it moving before it lands. Use conservation...

Hi, I have a physics assignment due, and I've been struggling with a particular question. I would really appreciate if anyone could please help. Homework Statement Consider the system below. The mp = 20.0 kg 'pulley' is a solid uniform sphere of radius of 0.250 m with the frictionless...

Homework Statement Consider the system below. The mp = 20.0 kg 'pulley' is a solid uniform sphere of radius of 0.250 m with the frictionless axle passing through its diameter. The mass of the block on the incline is m1 = 16.0 kg , and the coefficient of kinetic friction between the two...

Hi, I consider harmonic model of diatomic molecule: two atoms connected with a massless rod. Let one axis be along the rod, other two perpendicular to it. Let rotational velocity have components only trough perpendicular axes. In one book it is said that rotational energy of such diatomic...

Homework Statement [PLAIN]http://img189.imageshack.us/img189/5994/energyq.png Homework Equations This is a question by Monash University...i need to do part b by Energy conservation equations...but i don;t get the answer from that.. pleasez tell me how to do part b by Energy...

Homework Statement Consider the H2 molecule. The two nuclei (protons) have spin 1/2 and can therefore be in a total spin S=0 or an S=1 state. What is the orbital angular momentum of the two-nucleon system in the lowest energy state for the two values of the total spin? Homework Equations...

Homework Statement Rotation of a deformed nucleus is predicted to produce nuclear excited states with energies given by E(J)=J(J+1)hbar/2I. The first two excited states of 238 U are Jpi = 2+(0.045MeV) and Kpi=4+(0.148MeV). Show these energies are consistent with rotational excitation stating...

Homework Statement A pole P (300kg, length = 12m) is sliding on a frictionless surface at 8.28m/s. The pole's velocity is perpendicular to the poles length. A mass N (.5kg) collides with one end of the pole at 1043m/s and sticks. How fast does the pole rotate after the collision? Homework...

Homework Statement A gyroscope consists of a solid disk of diameter 1m and mass 100kg mounted on an axis passing through the center of mass of the disk. (a) Calculate the moment of inertia of the disk about its rotational axis. (b) What is the kinetic energy of rotation of the disk if its...

solved. thank you

Homework Statement The pulley in Fig. 9-25 has radius 0.150 m and moment of inertia 0.440 kg·m2. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00 kg block just before it strikes the floor. Figure: http://www.webassign.net/yf9/9-25.gif...

Homework Statement Five objects of equal mass are shown below together with the axis about which they are rotating. Select the objects in order of increasing rotational energy Solid Sphere, about any diameter, with R = 3 m and ω=5 rad/s Thin rod, about axis through center...

H2 has a moment of inertia equal to 4.603 x 10-48 kg m2. 1) Calculate its bond length. 2) For the first 3 rotational energy levels, find the a) l quantum number b) ml quantum number c) the degeneracy of each rotational level d) energy eigenvalues e) the magnitude of l Ok so I...

1. A uniform solid sphere of radius r starts from rest at a height h and rolls without slipping along the loop-the-loop track of radius R as shown. a) What is the smallest value of h for which the sphere will not leave the track at the top of the loop? Attempt: Homework Equations...

Homework Statement Four 60 kg skaters join hands and skate down an ice rink at 4.6 m/s. Side by side, they form a line 6 m long. The skater at one end stops abruptly, and the line proceeds to rotate rigidly about that skater. Find the linear speed of the outermost skater. The Attempt at a...

[b]1. A disk with radius of 0.3m and a mass of 4kg is free to rotate about an axle through its center. A cord wrapped around the circumference supports a weight with mass 5kg. a) What is the acceleration of descending mass if it is released? b) 5 seconds after release what is the...

Homework Statement Homework Equations The Attempt at a Solution Ride Designer A local carnival owner wants you to design a ride for him. Riders are strapped inside a rolling car which rolls down the track shown below. (sorry i can't copy the diagram) H=50m with 2 loops and...

Hi, I'm trying to understand the rotational energy of a fan impeller. I understand RE = 1/2Iw^2 So therefore an impellor with an inertia of 50 kg m^2 spinning at 1440 rpm = 568405 J my question is does this figure need to be divided by 3600000 J to give Kw hours?

i made a mistake, and fixed it, but I'm still wrong. I totally thought I had this one. Little help here. Homework Statement What is the minimum (nonzero) rotational energy of the ¹⁴N_2 molecule? Homework Equations E_rot = L * (L + 1) * E_0 * (m_e) / (4*M) M = (M_1 + M_2) /...

Homework Statement A rectangular loop of sides a = 0.3 cm and b = 0.8 cm pivots without friction about a fixed axis (z-axis) that coincides with its left end (see figure). The net current in the loop is I = 3.2 A. A spatially uniform magnetic field with B = 0.005 T points in the +y-direction...

Hello, I think I've got the right idea on how to perform this question but I just need a little bit of help. Homework Statement Show that for a rigid body rotating with angular velocity \omega the energy of rotation may be written as: E = \dfrac {1}{2}I\omega^{2} where the moment of...

Homework Statement Calculate the internuclear distance R0 for the HCL molecule from the fact that some of the lines of its pure rotation spectrum occur at wavelengths: 120.3 um, 96.0 um, 80.4 um, 68.9um, 60.4um. Assume 1H1 and 17Cl35 Homework Equations E_{ROT} = \frac{ hbar^2 } {2I}...

Homework Statement A dancer spinning at 72 rpm about an axis through her center with her arms outstretched. The distribution of mass in a human body is Head: 7% Arms 13% Trunk and legs: 80% Using your own measurements on your body calculate your a) moment of inertia about your spin b)...

In Physics I have a C average right now. These two quizes are my last chance at bringing my grade up to a B for this class. I have attached a copy of all of the problems that are on these two quizes totalling seven questions. THis is open book take home quiz where we can work with whoever we...

"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy. Homework Equations KE = 1/2 mv^2 U(potential) = -2U(kinetic) grav. potential =...

Homework Statement Humanity uses energy at the rate of about 10^{13} \rm W.If we found a way to extract this energy from Earth's rotation, how long would it take before the length of the day increased by 1 minute? Express your answer using one significant figure. Homework Equations...

A 250 g baseball is pitched at 35 m/s, and it's spinning at 55rad/s . What fraction of its kinetic energy is rotational? Treat the baseball as a uniform solid sphere of radius 3.8 cm. Answer in K_rot_/K_tot What the?! I am pretty lost on this one... Do I use K_rot_=(1/2)I\omega^2

Problem 10-58a: The equilibrium separation between the nuclei of the nitrogen molecule (N2) is 0.190 nm and the mass of each nitrogen nucleus is 14.0 u, where u = 1.66E-27 kg. For rotational energies, the total energy is due to rotational kinetic energy. Approximate the nitrogen molecule as a...

Three point masses lie along a rigid, massless rod of length L = 5.61 m : - Two particles, both of mass m = 2.1 kg, lie on opposite ends of the rod. - Mass M = 7.29 kg is in the center of the rod. Assume the rod lies along the x-axis, and rotates about the y-axis. about a point 1.28 m...

A thin, unirform rod (I=1/3ML^2) of length L and mass M is pivoted about one end. A small metal ball of mass m=2M is attached to the road a distance d from the pivot. The rod and ball are realeased from rest in a horizontal position and allowed to swing downward without friction or air...

Homework Statement A mass of 20 g is tied to one end of a thin thread. The other end is wrapped around a small cylinder of radius 0.01252 m. The small cylinder is attached to a much heavier aluminum disk. You calculated the rotational inertia of the aluminum disk in a previous problem in...

Homework Statement Problem reads: The pulley in the figure has radius 0.160 m and a moment of inertia 0.480 kgm^2. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor. Homework Equations...

Two astronauts (Fig. P11.51), each having a mass of 77.0 kg, are connected by a 11.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.40 m/s. (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum...

I am trying to understand how a charged object or an object with mass which is being accelerated by a linear field and therefore should accelerate in a purely linear fashion could possibly increase its rotational energy? I am not looking for trivial answers perhaps a certain distribution of...

The four wheels of a car have each a mass of 25kg and a radius of 30cm. The car's mass is 1000kg. We neglect the losses due to friction. We assimilate the wheels to homogeneous cylinders. a) What is the total kinetic energy of the car and the wheels if the speed of the car is 30m/s. b)...

I'm supposed to calculate the rotational energy levels of NH3, which is a symmetric rotator. The rotational energy levels are determined by the equation EJK = hcBJ(J+1) + hc(A-B)K^2, where J = 0, 1, 2,..., and K = 0, +/-1, +/-2,..., +/-J I don't quite get it. Are there a very limited set...

A cylindrical can of paint with (I = .5MR^2) starts from rest and rolls down a roof as shown in the link http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1424481748 Determine how far the can lands from the edge of the house. This is my work, but I...

I've got a turntable whose bearing is frictionless rotating at a certain speed. A mass of clay is dropped on to it and sticks a certain distance from the center. I've been able to calculate the new angular speed of the turntable after the lump falls on it, but the follow up question is to...