Circular motion about a central point or axis

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1answer
27 views

What happens to a 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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1answer
152 views

How can angular velocity be constant even when there is a torque by friction?

A cylinder at rest lying on a rough ground is given an impulse which imparts a translational velocity (no angular velocity) to it. The question goes ahead with finding time after which rolling starts ...
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1answer
158 views

Rotation motion like the number 8

I'm a college student majoring in culinology and I'm trying to find out the reason or method of the number 8 motion. Responses doesn't have to be in culinology examples, but that would be a great help ...
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1answer
33 views

how to calculate the angular velocity of ball from hitting angle?

i want to know how to figure out the angular velocity of ball in 2D when it's hit at a different known angles and constant force ? like in image ,and sorry if i had missed an info.
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1answer
155 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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0answers
128 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 ...
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1answer
167 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
65 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
138 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
24 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= ...
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1answer
327 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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2answers
42 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
40 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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2answers
87 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
12 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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0answers
58 views

Conjugate elements of $SO(3)$ group [migrated]

Composition of two rotations in 3d space yields another rotation $$R_1 R_2 = R_3, $$ and I can understand this by help of some figures in my book. So, the rotations in 3d space forms group. Then ...
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2answers
53 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
61 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
30 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 ...
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4answers
184 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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7answers
653 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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4answers
531 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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3answers
218 views

Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by: $$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$ $g$=acceleration due to gravity $\theta$=angle of inclined plane $k$=radius of gyration ...
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3answers
53 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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0answers
41 views

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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0answers
26 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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4answers
326 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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0answers
28 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
85 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
65 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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3answers
222 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 ...
2
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1answer
100 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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2answers
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What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
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0answers
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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
27 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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5answers
1k views

why does what get pushed away when centripetal acceleration is towards the center

If centripetal acceleration is towards the center, then why - when you spin a bucket of water (a classic demonstration) - does the water not get pushed out but rather stays in the bucket without ...
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0answers
31 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
84 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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1answer
260 views

Effect of Eath's rotation on a ball thrown upwards [duplicate]

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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2answers
46 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
50 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 ...
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1answer
51 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 ...
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1answer
49 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
31 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 ...
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1answer
50 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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0answers
32 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 $\mathrm{a}$: ...
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1answer
49 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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1answer
939 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
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1answer
59 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). ...