Circular motion about a central point or axis

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83 views

How can I set up an equation for distance traveled for a rubber band powered car?

I am to make a rubber band powered car, and I have to maximize it's distance traveled. The time taken to reach said distance, top speed of the car, acceleration of the car, is not relevant. I just ...
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2answers
111 views

Half-integer spin and infinitesimal rotations

On p. 692 of 'Quantum Mechanics' by Cohen-Tannoudji, he states that: Every finite rotation can be decomposed into an infinite number of infinitesimal rotations, since the angle of rotation can ...
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1answer
132 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
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2answers
73 views

Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
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1answer
88 views

Deriving Rabi rotation matrix

I want to understand where the matrix: $$ \left|\psi(t)\right> = \binom{a(t)}{b(t)} = \begin{bmatrix} cos(\Omega t/2)&-ie^{i\phi_L t}sin(\Omega t/2) \\ -ie^{-i\phi_L t}sin(\Omega t/2) & ...
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1answer
147 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
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2answers
334 views

EM Fields in a Rotating Frame of Reference

I'm struggling on my approach to the problem of figuring out E and B fields in a non-relativistic way for a rotating frame of reference in the x-y plane around the z-axis. I am attempting to do this ...
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1answer
76 views

Schriffer Wolff Transformation - for first order change in eigenvalues

Step 1 Let me formulate the problem to convey my notation. I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation $$ U_A A\,\,U_A^{-1} = A_{diag}$$ Now the matrix is ...
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1answer
386 views

Transform torque from Euler angles to infinitesimal Cartesian rotations

For a certain pair of rigid bodies, I have the gradient of energy in terms of Euler angles. I want to transform this gradient to the gradient of energy in terms of rotations about the $x, y, z$ axes ...
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69 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
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1answer
124 views

Symmetries of the action of the free classical Klein-Gordon field

I've read that the action for the free classical Klein-Gordon field $$S = \int \mathrm{d}^4x~ \mathcal{L} = \frac{1}{2} \int \mathrm{d}x^4 \left(\partial_\mu \phi(x) \, \partial^\mu \phi(x) - ...
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264 views

Increase in kinetic energy as some one walks to the centre of a merry-go-round?

When someone walks to the directly centre of a merry-go-round the total kinetic energy of the merry-go-round and person system increases. (assuming the kinetic energy due to the person walking to the ...
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0answers
132 views

Find the exact angle as a function of time for a rod that swings on a frictionless axle

This is a simple problem I thought of that I haven't been able to solve. Given a rod of uniform mass attached to a fixed axle, find the angle it makes with the horizontal if it is dropped from rest ...
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0answers
59 views

Stable planetary rotation states

In reading an article about theories as to how the slow retrograde rotation of Venus may have come into being, the article Why Venus Spins the Wrong Way (Franzen, 2001) stated that it is bound to ...
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0answers
2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
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74 views

Rotation in an 'empty' universe [duplicate]

Possible Duplicate: Is rotational motion relative to space? Assume a universe with the same physics as ours, but containing only one rotating (charge-free) body - let's say the size of the ...
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2answers
225 views

Does General Relativity correctly explain the ellipsoidal shape of the earth?

Does General Relativity theory correctly explain the ellipsoidal shape of the earth? It seems it does not because the Thirring expression¹ for the force of a spherical shell—of mass $M$, radius $R$, ...
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3answers
711 views

Maximum angular velocity to stop in one rotation with a known torque

I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that ...
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1k views

What point of application of force ensures more acceleration in a rod?

Suppose there is one rod and a force F is applied in two cases: Case 1: exactly at the middle on center of mass Case 2: at one end of rod In which case would the center of mass of rod be accelerated ...
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235 views

A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & ...
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3answers
3k views

Will a boiled egg or a raw egg stop rolling first?

If we roll a normal egg and a boiled egg at the same time on a floor 1) with friction 2) without friction which one will come to stop first (if they will stop at all) and why? Can anyone tell ...
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174 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
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287 views

Doubt concerning centripetal acceleration

What is the centripetal acceleration and angular velocity of a child located 8.2 m the center of a carousel? The speed (size of the tangential velocity) of the child is 2.1 m / s A train moves in a ...
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210 views

rotation matrix - why am I thinking this wrong?

The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix. $$ \begin{array}{lcl} x' &=& x \cos\theta - y \sin\theta \\ y' ...
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2k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
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3answers
67 views

Why does earth spin counter-clockwise?

If we observe the earth from the north pole, we can see that the earth is rotating counter clock wise direction. The earth spins due to angular momentum, but why only in counter clock wise. Why ...
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1answer
48 views

Warship cannons influence on speed/direction [closed]

I've been looking at great warships like the Iowa or equivalent ww2 warships, and I raised question. This kind of war is pretty much only about strategic placements, accuracy and fire power. Hence ...
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1answer
46 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
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2answers
28 views

Stroboscope's unit

Can someone please tell me why does stroboscope's unit is rps or rpm. Revolution per minute/second. Although the stroboscope used was an electronic stroboscope. Is it has something to do with the ...
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1answer
36 views

Specific scenario involving rotation and inertial frames of reference?

We recently went over some rotational motion in my freshman physics class, I had a question for the professor on your frame of reference, and how that would effect the rotation of the object. Say you ...
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1answer
53 views

Motion of a rigrid body: Why is motion only a compostition of two forms: rotation and Translation?

If you are in a 2-D space the motion of any rigrid body is composed of 2 different things, namely rotation and translation. If you are in 3-D space the motion of any rigrid body is also composed of 2 ...
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1answer
51 views

Rotational Speeds

I was driving the other day and couldn't help but look at all the wind mills in the wind farms. I know I am not doing the math correctly, but I want to know what is "really" happening when a windmill ...
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4answers
266 views

Gravity doesn't seem to work the way it is supposed to [duplicate]

This has been a bit of an awkward question that's been plaguing me ever since I started watching space documentaries on discovery about 10 years ago. I was saving this for the day I would ever meet ...
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3answers
741 views

Is there a difference between “average acceleration” and centripetal acceleration?

Question adapted from Examkrackers MCAT prep book: A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the ...
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2answers
225 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
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2answers
322 views

What happens if the earth stops rotating? [duplicate]

I was wondering what would happen to all the components on the surface of the Earth if the Earth suddenly stops rotating but does not stop revolving.
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1answer
58 views

A pretty dumb question on observation

Very often I have seen, that a bicyclist can balance himself better, while in motion, than he can while at rest(with his legs on the paddles of the bicycle). Now, I know that objects, say, a disc ...
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2answers
67 views

Kinetic energy of a mass rotating about two axes

I'm working on a question where I have to find an equation for the kinetic energy of a mass being rotated by a fold-able arm. The equation for $m_1$ is obvious, however, the equation I derived for ...
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1answer
148 views

Can we calculate the frame dragging force of the Earth?

Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?
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1answer
4k views

How do I calculate the experimental and theoretical rotational inertia of a point mass?

I'm getting some weird results from a calculation I'm doing and quite honestly, I'm pretty sure it's due to human error. I do have an apparatus involved for the experimental process for my lab but I ...
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2answers
3k views

Slowdown rate of rotating body due to friction force [closed]

This isn't a homework question, but it might as well be. The problem I have been pondering is: If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
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2answers
210 views

Relativistic Lagrangian transformations

I need to study the relativistic lagrangian of a free particle. It's $\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
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1answer
35 views

How does Foucault's pendulum work in a place other than the poles?

I find it easy to understand how Foucault's pendulum works at the poles, the pendulum oscillates in a fixed plane and we, along with the earth, rotate around it. So it appears that the pendulum's ...
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1answer
20 views

Euler Angles with respect to base body when Euler Angles with respect to another body is known

Let's say I have a fixed base body $B_0$ with a reference frame $X_0Y_0Z_0$, and two other bodies, $B_1$ and $B_2$, rotated arbitrarily with respect to this base body. Coordinate systems fixed to ...
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4answers
144 views

Infinitesimal Rotations

Have a little question regarding infinitesimal rotations. In the Cohen Book, volumen 1, Complement B-VI, it says that the transform of a vector $\textbf{OM}$ under an infinitesimal rotation can be ...
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1answer
30 views

Patterns in a spinning wheel [duplicate]

Why do we see patterns on a rotating wheel with spokes which seem to rotate counterclockwise or clockwise as and when the wheel accelerates or deaccelarates. What I mean is the patterns like this
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1answer
21 views

Determining the three Euler angles from the acceleration

I want to know, given the measurement of an accelerometer at rest (so not really an acceleration but a force per unit of mass) the inclination of this accelerometer, along the three axis. For this, I ...
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1answer
69 views

Angular velocity and instantaneous rotation axis

Let's suppose that we have a cylinder of moment of inertia $I$ rolling on the floor without sliding, moving with linear velocity $v$ and rotating around an axis passing through the center of mass with ...
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1answer
107 views

Euler angle rotation - active/passive

I have a very simple problem, that I cannot wrap my head around and is hurting my brain. I have a very simple example of the problem, please consider the the figure below: In the first picture, you ...
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1answer
80 views

Physical interpretation of diffeomorphism from $SO(3)$ to $\mathbb R \mathbb P^3$

I am not good at picturing either $SO(3)$ or $\mathbb R \mathbb P^3$, the latter denoting the real projective space. Can someone give me a rough physical understanding of the geometry and implication ...