Circular motion about a central point or axis

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Clarification regarding Eq. (2.6.21) Weinberg Vol. 1

While reading the action of time reversal operator for massless particles, I was going through the derivation for Eq. (2.6.21) from Weinberg Vol. 1 which proceeds as follows $$ \begin{aligned} U^{-1}(...
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15 views

What force is needed to turn the Earth Pole-over Pole. Eg. UK now on Equator? [closed]

Specifically, if someone could specify the Joules energy required to force the Earth to slowly rotate the poles end-to-end by say 1 degrees rotation, and by 5 degrees. To be clear I mean to literally ...
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1answer
74 views

Understanding Euler's rotation theorem

According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will ...
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100 views

Will future spaceships for very long distance rotate?

I have seen in the movie Interstellar and The Martian they use the model of spaceship which rotate around it's axis. This is the spaceship model from Interstellar. This is spaceship model from The ...
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Feasiblity of a long spinning top using an electromagnet to pull on Earth's magnetic field

Would it be feasible to build a infinitely spinning top (ref. Inception) by including a battery powered electromagnet who's polarity flipped in sync with the top's rotation such that the pull against ...
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1answer
60 views

Rotational motion: A cylinder, sphere and hoop rolling down a ramp [closed]

I have a question about comparing different objects in rotational motion. In this scenario: A cylinder (with moment of inertia = $\frac{1}{2}MR^2$), a sphere ($\frac{2}{5} MR^2$) and a hoop ($MR^2$) ...
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1answer
31 views

Can a tidally locked planet have a horizontal rotational axis?

Is it hypothetically possible for a planet to be both tidally locked, and still have a rotation "horizontally"? Where the substellar point would in effect be like the point of a top, spinning and yet ...
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2answers
83 views

Energy of a body in circular motion?

I'm confused about energy of a body in circular motion. In particular I'm having trouble to find the correct answer to this question. Consider the body in the picture that is set in motion from ...
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26 views

Angular velocity in body frame to displacement in lab frame?

For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis: $$ \omega_1 = w_1 \cos (w_3 t) $$ $$ ...
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2answers
55 views

Does orbital motion cause rotation?

Assume the moon was flying freely in space, and not rotating at all. If if then happened to pass earth at just the right distance and velocity to fall into orbit, would its absolute rotation be ...
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71 views

Rolling Resistance Coefficient

I found that rolling resistance can be expressed with this equation: $$F_\mathrm{rr} = \frac{C_\mathrm{rr} W}{r}$$ Where $C_\mathrm{rr} =$ coefficient of rolling resistance $W =$ normalforce $r =$...
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47 views

Angular acceleration from torque and radius

The story is about wheel. I have a wheel and I need to know it's actual angular velocity(which doesn't mach Vcar_longitudal / r). What I have access to is torque ...
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2answers
61 views

What happens to a body if it rotates extremely fast?

I am thinking on a object, e.g. ball or planet that starts rotating with increasing speed. Let's assume that his speed get's closer to the speed of light, what happens to this object? There are ...
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75 views

Change of Earth's Rotation [closed]

At the time of global warming, all the ice will melt, resulting the reduction in spinning of earth, Initially. But, if earth's surface temperature rises continuously for a long time, exactly this will ...
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1answer
73 views

Vectors finding direction include the difference between “north of east” and “east of north”

In what direction is your friend from the starting point after skiing 3 km east and then 1.5 km north? so far I know that angle= tan-1(opp/adj)=(1.5/3.0) angle= 26....
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2answers
225 views

What is the difference between vortexing and centrifuging?

I understand that vortexing will result in mixing / re-suspension of particles, and that centrifugation will result in the separation of particles. However, what is the difference in the physics that ...
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1answer
51 views

How to show the finite rotation of a spin-1/2 system?

I'm reviewing my quantum mechanics by going through Sakurai and Napolitano again and working out all of the derivations. I'm stumped (though I probably shouldn't be) on some algebra in the finite ...
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130 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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1answer
68 views

Angular velocity when a rod inclined to a wall slips and its subsequent motion observed from the axis of rotation

When a rod inclined to a wall slips, rate of change of which angle does the angular velocity represent? Is it the rate of change of angle with which the rod is inclined to the horizontal ? I'm not ...
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210 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
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66 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
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1answer
64 views

To prove uniqueness of Rotation Tensor [closed]

How can you prove that a rotation tensor which rotates some given vector is a unique tensor? Let's say we have a vector 'a' and we take a tensor product of that vector with some tensor 'Z' such that: ...
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1answer
33 views

What effect will a space-elevator have on earth's rotational speed?

If you (or e.g. a skater) spin on the spot with your arms outstretched you spin at a given speed, but when you retract your arms you spin much faster, extending your arms again will slow the spin down....
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4answers
273 views

Bicycle counter-intuitive: in which direction it will move? [duplicate]

I saw this puzzle in a local newspaper: Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the ...
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3answers
66 views

Kinetic energy of a rotating object

in an exercise, a linear molecule is being subject to a force applied on the edge in its axis. Then $K_1=\frac{1}{2}mv^2$, all is well. Then in the second point of the exercise, the force is applied ...
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Euler angles and curvilinear coordinate systems

If I have a curvilinear coordinate system and supposing I impose the condition that back transformations to Cartesian coordinate system are not permitted. I perform a rotation of the three axes( say ...
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63 views

Parallel axis theorem non-uniform density [closed]

The parallel axis theorem says that if the moment of inertia of a body rotating about the body's centre of mass is $I_{cm}$, then the moment of inertia of the body rotating about an axis parallel to ...
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57 views

Correct formulas for two wheeled robot motion

I'm trying to write a simulation of a two wheeled robot, which can be controlled by varying the speeds of his wheels, independently. However, the physics engine that I'm using can only rotate a body ...
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1answer
186 views

Change in acceleration due to gravity because of rotation of earth [duplicate]

The formula above is the equation for acceleration due to gravity when earth rotates. G is the original acceleration. Can someone explain how this formula came?
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2answers
89 views

What is the difference between translation and rotation, in the Lagrangian/Hamiltonian frameworks?

This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian ...
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1answer
105 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
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30 views

Considering rolling without slipping using axis at contact point with surface

For a ball rolling down a ramp without slipping, we can use $\Sigma \tau = I \alpha$ about two axes: an axis through the center of the ball, and an axis through the contact point with the surface. The ...
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1answer
47 views

In golf, is there a rotational mechanical advantage of using a thicker grip?

I was asked to migrate this question to the physics exchange. Ok, so many professionals are now using the new SuperStroke golf grips. I am basically thinking about the concept of a bigger grip, but ...
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65 views

Accelerometer reading in a uniform circular motion

Question - there is an accelerometer kept in a car moving in a uniform circular motion. The accelerometer is kept in such a way that the z axis points downwards, x axis is pointing towards centre of ...
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1answer
199 views

Rotation of fluid filled cylinders [closed]

Given two cylinders of same mass , one completely made out of solid metal and the other a hollow one which has been filled with a viscous fluid say oil. Both have the same mass.Now if they are placed ...
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3answers
256 views

Coupling between galaxy spin and central black hole spin

What is the relationship between the spin of a galaxy and the spin of its corresponding black hole? Associated questions: Do they always have the same axis of rotation? Do they always spin in the ...
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1answer
53 views

Why is the axis of rotation about O? (picture)

I'm not understanding part b. Why is the rotation about O? Shouldn't it be about C? If you do it about C you get a different answer because you'd get the same angular velocity but a different radius ...
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106 views

Pauli Matrices & 2D Rotation Operators?

I was doing a strange calculation with my teacher the other day: find the eigenvalues and eigenvectors of the 2D rotation operator. Intuitively, there should be no solution to this problem in $\mathbb{...
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1answer
130 views

Relative speed of Geostationary satellite with respect to earth?

I was wondering whether relative speed of geostationary satellite with respect to earth is zero or not.Since angular velocity of satellite about earth is same as angular speed of earth about its own ...
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1answer
32 views

Euler Rotattion for j$\geq$ 1

I am trying to understand Euler Angles as given in Sakurai. Specifically, with the case j=1, where it is stated ($\hbar=1$) For j=1 ONLY, we can replace exp(-i$J_y\beta$)$\rightarrow 1-J_y^2(1-\...
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60 views

Why don't we include angular acceleration while calculating net acceleration for a particle moving in a circle ?

When we calculate net acceleration of a particle It is the vector sum of the centripetal acceleration and the tangential acceleration (if any) however why don't we also consider adding angular ...
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1answer
73 views

2 men support a uniform horizontal beam at its 2 ends .If one of them lets go ,the force exerted by the beam on the other man will?

A) remain unaffected B) increase C) decrease D) become unequal to the force exterted by him on the beam This was a question in one of my books for mechanics, they solved the question using ...
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33 views

Rotation of Spin-operator

I have to calculate the rotated Spin operator and been given the equation for the Rotation Matrix $R(\Theta,\mathbf{n})$ as well as its action on an arbitrary vector $\mathrm{a}$: $R(\Theta,\mathbf{...
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1answer
51 views

Explaining conservation of angular momentum with a disconnect

A probe is rotating in space and an instrument comes loose and disconnects. I need to explain why the angular velocity $\omega$ of the probe does not change. This equation describes how the angular ...
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38 views

Why do linear momentum and angular momentum have to be conserved in ground frame only?

According the Newton's second law of translational and rotational motion respectively if the net external force /torque acting on a body is zero then the linear/angluar momentum is a constant . So ...
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Astrophysics of spirals [duplicate]

What accounts for the structure of spiral galaxies? I would seem that, considering gravity is proportional to distance, outer objects could not be connected in any way to inner objects (ie. a spiral) ...
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1answer
65 views

If, for a body rolling on an incline, the friction coefficient isn't enough to allow pure rolling will it still roll?

More specifically that it won't be pure rolling (obviously) but would it still have some rotational motion along with its translational motion? (if yes how would we write their mechanical equations). ...
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1answer
34 views

When applying the equation of torque and equating it to $I\alpha$ which moment of inertia do we take?

I believe $T=I_{cm}\alpha$, where $I_{cm}$ is the moment of inertia about centre of mass and $\alpha$ is the angular acceleration. But do we take $I_{cm}$ even if the torque has been taken about a ...
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1answer
23 views

Equation for Turning Projectile

I'm trying to cook up an equation that will give me position for a projectile which operates in the Newtonian Domain. So a the fall equation is: $$\mathbf{p_t} = \frac{\mathbf gt^2}{2} + \mathbf{v_0}...
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1answer
99 views

How is this seemingly counterintuitive result in a rotation problem explained?

In the classic spool problem, where a spool of string of mass M is unrolled with a force F, like in the diagram, after working through the equations with Newton's laws of rotation and translation, we ...