Translational Definition and 173 Threads

The kinetic energy of a rotating rigid body is given by K=1/2mv^2 + 1/2Iw^2 but how to determine the proportion of translational energy and rotational energy? I know that if the mass distribution is more concentrated at its center mass, then more energy goes to the translational part. But is...

According to the virial theorem, $$\left\langle T\right\rangle =-{\frac {1}{2}}\,\sum _{k=1}^{N}{\bigl \langle }\mathbf {F} _{k}\cdot \mathbf {r} _{k}{\bigr \rangle }$$ where ##N## is the number of particles in the system and ##T## is the total kinetic energy. It is often claimed that this...

Below is a pulley with mass and a string around it where the tension of one end of the string is 20 N and the tension of the other end of the string is 60 N. I know there is a net torque due to the differing tensions of the string, so I am wondering what the translational forces are on the...

Why is the total energy energy equal to the sum of translational kinetic energy and rotational kinetic energy? I understand the derivation KE = 1/2 I w^2 for a rigid object rotating around an axis: sum 0.5 * m_n * (v_T)^2 = sum 0.5 * m_n * (wr_n)^2 = 0.5 * w^2 * sum m_n r_n^2 = 0.5 * I * w^2...

Take a single atom in a vacuum chamber at T=0 K. The atom is motionless. Add thermal energy to the vacuum chamber. Does this cause the atom to move? If so, by what mechanism?

If this question asked for internal energy, then it is a straightforward thing, just use the formula U = (3/2) nRT = (3/2) PV. But the question specifically asked for average translational kinetic energy which I'm stuck with the value of T to plug in into the formula as the question only give us...

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?

A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities...

Dear Experts, I have read from various sources that the temperature of a gas is related to the "average translational kinetic energy" of a molecule of gas. When there are molecules that support motion other than translational ,which may also have rotational and vibrational motion, How does those...

What would the world look like if there was no translational symmetry? How would certain laws be different and what wouldn't change?

Imagine a long brick in outer space. You apply a force tangential to the center of mass. The brick accelerates in a transitional and angular fashion. There are no constraints or fixed axis. How would I calculate the translational and angular acceleration? I would like to run some simulations...

I'm a bit confuse. In chapter 15, of Conceptual physics by Paul Hewitt: "Temperature is related to the random motion of atoms and molecules in a sub- stance. (...) More specifically, temperature is proportional to the average “trans- lational” kinetic energy of random molecular motion (motion...

Homework Statement "Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per...

A flying object is moving in 3D space having translational velocity and the object is also rotating. Consider a body frame (xb-yb-zb) attached to the C.G of the moving body. Hence the body attached frame is also translating and rotating (as the object is flying) with respect to a fixed inertial...

Homework Statement Find the acceleration of each object. Note: the question mark in the diagram should be θ (angle of inclined plane) 2. Homework Equations τ = F . r Στ = I . α α = a / R ΣF = m . aThe Attempt at a Solution For object A: ΣF = m . a TA - WA sin θ = mA . aA TA - mA . g. sin θ...

Can anyone explain what does the author mean by the statement below? page 27 of this paperI don't understand the relation between the Fourier transform and translational invariance. Thanks

Homework Statement The ammonia molecule (NH3) has a dipole moment of 5.0×10−30C⋅m. Ammonia molecules in the gas phase are placed in a uniform electric field E⃗ with magnitude 1.3×106 N/C . Part A: What is the change in electric potential energy when the dipole moment of a molecule changes...

Homework Statement Consider a system of objects labeled by the index ##I##, each object located at position ##x_{I}##. (For simplicity, we can consider one spatial dimension, or just ignore an index labeling the different directions.) Because of translational invariance ##x'_{I}=x_{I}+\delta...

Homework Statement The problem is attached in the file "selection(1).pdf" The explanations/solutions are attached in "selections.pdf" which is below [Problem image - added by moderator to make it visible in-thread] Looking at how they solved part C, I have no idea why they say that the...

I have really problem with equation of the root – mean – square (rms) speed of the gas molecules when we use the universal gas constant (R) mentioned in all references. Accordance to all reference books, we have below equation for the total translational kinetic energy: Vrms = (3RT/ M)^0.5...

Homework Statement The screen shot I have attached is the original question, I think I'm ok up until the Ne part. My answer just seems like a ridiculous number, I haven't had much experience with this so don't really know what an 'normal' KE for 1kg of gas would be. Homework EquationsThe...

Hi. I'm trying to take a purely translational approach to precession (i.e. not using angular momentum and torque). I'm looking at a gyroscope that consists of four point masses on a cross and at a moment in time when one mass is at the topmost point (see sketch). I'm assuming a virtual...

Homework Statement In studying for an upcoming exam, one of the concepts introduced was that an object moving translationally will move faster than one moving rotationally. To me that doesn't make sense. So, I do not have a specific problem but really just looking for someone to be able to...

I feel like this is a very simple concept that I seem to confuse more often than I'd like to admit. Namely, if you have a rotating simple pendulum (or really any object), why does it have 0 translational kinetic energy if it is kept rotating around a fixed axis? The centre of mass is constantly...

Homework Statement A uniform rod of length b and mass m stands vertically upright on a floor and then tips over. a) Assuming that the floor is rough (i.e., the end of the rod that is initially touching the floor cannot slip), what is the rod’s angular velocity when it hits the floor? 2...

Hello! :) When solving a problem, I had to calculate the angular velocity of a homogenius rod when it comes to vertical position, after being released from a horisontal position (the rod is fixed at one end). This is as usually done with energy conservation, using the rotational energy of the...

Homework Statement A trailer carrying a boat is supported by a scale which initially reads 48 kg. The boat (and therefore its centre of gravity) is moved 0.15 m further back on the trailer. The scale now reads 37 kg. Find the mass of the boat (Ignore the 6.0 m distance because it was not given...

Hello, I'm trying to figure out the free body diagrams for the inverted pendulum problem and I'm having trouble figuring out the one equation: ##Psin\theta + Ncos\theta - mgsin\theta = ml\ddot{\theta} + m\ddot{x}cos\theta## I've never really seen a mixed sum of forces equation before where some...

The Hamiltonian is not always equal to the total energy. In fact the Hamiltonian for a system of particles could be defined as ##H=L-\sum \dot{q_i}\frac{\partial L}{\partial \dot{q_i}}## Which is the total energy only if the potential energy is a function of ##q_i## and if the kinetic energy...

Hi guys, i have been confused by one statement on the spatial correlation funciton in the statistical physics textbook. They say for a spatial correlation function f(x1,x2), where x1 and x2 are the coordinate of particle 1 and 2, if the system has translational symmetry, then f depends only...

Hi, Suppose a force of 5N is being applied to a 5kg block and the force of friction from the surface on which the block is in motion is 5N as well. The Net Force of the block is 0N, thus the block is not accelerating and is moving at a constant velocity. The question I have is, how to...

Homework Statement Given: Wheel radius is 20 CM, Gear radius is 5 CM, Coefficient of Static Friction is .2, Weight on rear wheel is 50 N. What is the minimum force that must be applied to the pedal for the wheel to begin accelerating on a level surface?Homework Equations Net T = I * a T = R X...

Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's...

Hello Everyone, Let us think about a rod whose length is L and end points are A and B. The road is parallel to the ground therefore the weight of the rod is perpendicular to the line between A and B. The weight of the rod is F and two forces with the magnitude of F are exerted on both ends and...

1. Problem: Determine the final translational speed of a spinning disc that is dropped on an infinite horizontal plane. Think of spinning up an automobile wheel suspended over a road (wheel spinning normal to the road), then dropping the wheel on the road. When the wheel rim touches the road...

Homework Statement This is a conceptual question about a prior assignment I had: A thin spherical shell rolls down an incline without slipping. If the linear acceleration of the center of mass of the shell is 0.23g, what is the angle the incline makes with the horizontal? Homework Equations...

Homework Statement A frictionless pulley has the shape of a uniform solid disk of mass 5.00 kg and radius 28.0 cm . A 1.40 kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the stone is released from rest. As it falls down, the wire unwinds without...

Suppose I have some sort of rigid body, a solid sphere let's say. For simplicity's sake let's assume that the sphere can only rotate about a single arbitrary axis through the center of mass. If the center of mass of the sphere is traveling with a constant velocity (with respect to some arbitrary...

In the figure A has mass 4 kg. B and C are identical uniform discs, each of mass 2 kg. The string supporting A is ideal. Obtain the acceleration of A I have just one question, Why is pulley C undergoing translational motion ?, it should be rotational motion because it rotates about a fixed axis

While I am familiar with the derivation of the relationship between mean translational kinetic energy, ##<E_k>##, and temperature, ##T##, for an ideal gas (namely ##<E_k> = \frac{3}{2}k_B T##); I fail to see how we can establish such a relationship for solids, liquids, and even real gases. Could...

Thoughts on this? http://journal.frontiersin.org/Journal/10.3389/fgene.2014.00140/full The codon redundancy (“degeneracy”) found in protein-coding regions of mRNA also prescribes Translational Pausing (TP). When coupled with the appropriate interpreters, multiple meanings and functions are...

Hi Everyone, I'm having some trouble with a problem concerning translational and rotational equilibrium. The question involves a balance with various masses suspended from it (see attached image). The question states that the counterweight is moved from 1cm away from the fulcrum to 2cm away from...

https://www.physicsforums.com/attachment.php?attachmentid=67320&stc=1&d=1394121524 So the initial potential energy is equal to the final potential energy plus rotational kinetic energy, right? Is the final translational kinetic energy also considered if energy is conserved? Thank you very...

Homework Statement I'm given the following diagram And asked to find the transfer function G(s) = \frac{X(s)}{T(s)} and seem to be having some difficulty doing so. Homework Equations The Attempt at a Solution Apparently this is free body diagram I seem to be having difficulty...

The velocity of any point P of a rigid body in rotation plus translation is \vec{}vp=\vec{}vCOM+\vec{}vp,COM. Now |\vec{}vCOM|=v and \vec{}vp,COM =rω . But v and rω are same thing as v=rω ,so velocity of the particle every time will be √2 v.Then what is the difference between \vec{}vCOM and...

Homework Statement Two copper cylinders, immersed in a water tank at 30.3 °C , contain helium and nitrogen, respectively. The helium-filled cylinder has a volume twice as large as the nitrogen-filled cylinder. a) Calculate the average translational kinetic energy of a helium molecule and...

Hello, I am trying to understand a short literature article (doi: 10.1021/ja01635a030). I am not sure how much liberty I have to reproduce its contents here, and I can't explain it here because I don't understand it -- which is why I have this question. I believe it is proposing that a...

I am having a hard time proving this to myself: Given some object with a known inertial moment and center of mass, with r = distance from COM, do forces of equal magnitude along some line L perpendicular to R all yield the same F_t (translational force) and F_r(rotational force), and how can...

A hollow, thin-walled sphere (ICM = 2MR2/3) of mass 20 kg is completely filled with a liquid of unknown mass. The sphere is released at the top of a plane inclined at 30° to the horizontal, and it rolls 20 m to the bottom in 3.6 s. What is the mass of the liquid? 2.My approach is...