Circular motion about a central point or axis

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2answers
65 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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3answers
349 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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1answer
40 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
53 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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0answers
23 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
60 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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1answer
72 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
150 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
43 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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2answers
110 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
48 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
108 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
38 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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2answers
56 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
63 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: ...
0
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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 ...
4
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4answers
243 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
806 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 ...
2
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3answers
63 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 ...
2
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0answers
44 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
46 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 ...
7
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4answers
381 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
48 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 ...
2
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1answer
149 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?
3
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2answers
83 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 ...
9
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3answers
238 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
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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2answers
2k views

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
27 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
40 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 ...
0
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0answers
47 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
154 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
320 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 ...
0
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2answers
52 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
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 ...
0
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1answer
90 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 ...
0
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1answer
61 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
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 $\mathrm{a}$: ...
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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 ...
5
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1answer
963 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
61 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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0answers
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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0answers
16 views

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) ...
0
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1answer
33 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} + ...
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1answer
80 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 ...
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1answer
207 views

Understanding rotational motion on a rough surface

I am having trouble gaining an intuitive understanding of rotational motion for an object rolling on rough surface, and I have a few questions regarding it. Let's say that there's a cylinder that ...
1
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0answers
61 views

What does hinge reaction mean ? How do i calculate it? [closed]

I recently came across a lot of problems where components of Hinge Reaction were asked along different axis . My questions are : A) What does hinge reaction mean ? B) Does it change ...