Circular motion about a central point or axis

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39 views

Angular velocity relative to different frames

In Goldstein it is said "It is intuitively obvious that the rotation angle of a rigid body displacement, as also the instantaneous angular velocity vector, is independent of the choice of origin of ...
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3answers
65 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
117 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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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
319 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
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1answer
34 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
24 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
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4answers
1k views

Will the sea form a concave surface?

Without neglecting the fact that the earth is rotating, let us be in a ship (such that there is no relative motion between sea and ship) in a sea that surrounds the northern most or southern most ...
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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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1answer
64 views

Negative sign in rotation operator again

In Wikipedia's page on the rotation operator, section "In relation to the orbital angular momentum", they write $$ R(z,t) = exp((-i/h) \varphi L_z) $$ where $\varphi$ is the angle being rotated ...
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1answer
95 views

Rigid Body Dynamics - Calculating Rotation of an Object

I've looked everywhere and I can't quite find a concise answer, especially due to my limited knowledge and understanding of terminology. I found something called Rodrigues' Rotation Formula that ...
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2answers
102 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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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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3answers
435 views

Would this box on the floor rotate based on friction?

There is a floor that friction is proportional to its velocity (like $F=-kv$) and there is a box with its width as $l$ and its height as $h$. (you may assume that $l$ is longer than $h$). It is on the ...
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0answers
17 views

Why do rotating devices make air colder? [duplicate]

I end up thinking this question frequently recent days. It seems an easy question but i cannot find the answer. You could say "faster the air, cooler it becomes" in that case i am expecting an ...
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0answers
18 views

Cylinder rotating inside another cylinder. [duplicate]

A homogeneous cylinder with radius a and mass m rolls in a hollow cylinder with radius R. Determine the kinetic energy of the cylinder as function of $\dot{\theta}$. I'm sorry for ...
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1answer
60 views

Moment of Inertia of Water. [closed]

Determine the moment of inertia $\Theta$ of a water molecule ($m_H=m,m_O=M$) for a rotation around the axis which is perpendicular to the molecule plane and goes through the center of mass S of the ...
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1answer
47 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
70 views

Only get part of commutator form expanding to third order in generator expression

(Shankar 12.2.4) Let $U[R(\epsilon_z\hat k)] = I - {i\over\hbar}\epsilon_z L_z$ be the infinitesimal generator for rotation operators, and $T(\vec\epsilon) = I - {i\over\hbar}\vec\epsilon\cdot\vec ...
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1answer
19 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
33 views

On application of angular momentum conservation laws

Consider a situation like this: a massless ring is kept fixed at rest on a horizontal plane. A massless thin string attached at its one end to a point on the circumference of the ring while its other ...
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1answer
29 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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3answers
7k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
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1answer
76 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
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2answers
118 views

Torque required to rotate panel on one axis

I am working on a project that requires solar panel to rotate around its axis, but I am struck with deciding the specs of the Servo Motor that is capable of doing this. Though, the panel hangs on its ...
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0answers
41 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
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7answers
468 views

Can a ultracentrifuge be used to test general relativity?

With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to ...
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0answers
127 views

Earth magnetic field [closed]

I gather that, in these days, the most common explanation for the Earth magnetic field existence and strength is the theory of convetive currents of molten iron and nickel atoms in the outer core of ...
2
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1answer
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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4answers
1k views

Simple Harmonic Motion - What are the units for $\omega_0$?

I'm trying to understand the units in: $$mx''+kx=0$$ And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring ...
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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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3answers
96 views

Rotation in the x-t plane

I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation ...
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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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2answers
48 views

Spring on a rotating disc [closed]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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0answers
30 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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2answers
110 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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3answers
633 views

Object moving in a circular path without accelerating

A train is moving with a constant speed on a straight portion of track. Then, it encounters a curve in the tracks, and goes along the curve. However, it does not change the magnitude of acceleration ...
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12answers
3k views

How can the contact point of rolling body have zero velocity?

They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion?
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1answer
65 views

Angular momentum-torque relationship in a rotating frame?

I have read that $$\vec\tau=\frac{\mathrm{d}\vec L}{\mathrm{d}t}$$ holds true whenever the origin is not accelerating. But I cannot see why this holds true for a rotating frame of reference (such as ...
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2answers
172 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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1answer
70 views

Effect of Eath's rotation on a ball thrown upwards

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
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0answers
30 views

A free axis of rotation

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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1answer
240 views

Would time dilation cause a planet to rotate?

For the sake of the argument lets use a black hole so the time dilation effects are greater and the planet in question is orbiting close enough to have significant TD effects but far enough to not ...
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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
37 views

Starting point for a derivation of fictitious forces

I came across this expression at the start of a derivation of fictitious forces: $$(dA/dt)_L = (dA/dt)_R + \omega \times A$$ Where the $L$ subscript refers to the laboratory (inertial) reference ...
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3answers
1k views

Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram. Would an ...
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1answer
40 views

force acting on a small point mass dropped over a rotating rigid body

I came across a situation where I must find the force exerted by a rotating rigid body on a point mass $m$, dropped over it. The rotating rigid body will smash the point mass away in a direction ...
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1answer
116 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...