Circular motion about a central point or axis

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2
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1answer
190 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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2answers
55 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 ...
1
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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 ...
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4answers
239 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 ...
2
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3answers
62 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
45 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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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
144 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
81 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 ...
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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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 ...
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 ...
0
votes
1answer
151 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 ...
9
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3answers
237 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 ...
0
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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 ...
1
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1answer
69 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 ...
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 ...
0
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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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2answers
51 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 ...
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 $\mathrm{a}$: ...
0
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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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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) ...
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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). ...
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 ...
0
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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} + ...
1
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1answer
78 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 ...
1
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1answer
203 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 ...
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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 ...
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2answers
91 views

Rotation of a system of two masses [closed]

A uniform disc of mass M and radius R is suspended vertically by a pivot at its periphery. A particle of mass M is fixed to the rim and raised to the highest point above its center. The system is ...
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0answers
112 views

Tension in a rod rotating about a fixed point

A rod of mass $m$ and length $l$ is rising about a fixed point in the ceiling with an angular velocity $\omega$ as shown in the figure. Now, on taking a small element on the rod, the net tension ...
0
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1answer
107 views

Is angular acceleration same about all points of a rotating ball?

Suppose a ball is rotating due to force $F$ applied at its top (on a rough ground).There is pure rolling. In one case we write the equation w.r.t COM i.e $F.R=I(\alpha_1)$ and $F-f=ma$ and ...
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2answers
183 views

Need help understanding angular acceleration due to gravity

The question asks what the angular acceleration of an uniform disc of radius $R$ rotating about an axis passing through its edge if it is released from rest with its center of mass at the same height ...
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2answers
104 views

Prove that a translation operator times a reflection operator is unitary and Hermitian [closed]

I am trying to prove some properties of the product of the (unitary) translation operator $\hat{T}(a)\psi(x) = \psi(x-a)$ and the (Hermitian) reflection operator $\hat{R} \psi(x) = \psi(-x)$. In ...
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1answer
27 views

How to spatially rotate the frame of reference Faraday Tensor? Special Relativity and Galilei Transforms

Hey I'm currently just starting out doing special relativity and I stumbled upon following problem: If I have the faraday antisymmetric tensor $F^{\alpha \beta}$ and I perform a spatial rotation of ...
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0answers
47 views

Confusion in Special Relativity: Rotating frame of reference

Suppose we are observing a rotating frame from an inertial frame, free from gravity, and try to measure the circumference of a circle drawn in the rotating frame. Since our measuring rod would be ...
0
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1answer
82 views

How does the tension force of a massless string affect the speed of a mass on its end?

i,j, and k are the unit vectors in the following question, and $\omega$ is the angular velocity. Lets say you have a mass m attached to a mass-less string of length $L$ tied to a peg with no ...
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1answer
84 views

How to conserve angular momentum?

If i want to conserve angular momentum from the point of contact of the solid sphere and the ground how should I do it? I know we can use $mvh = I\omega + MvR$ ,if the collision is elastic. But in ...
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3answers
340 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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0answers
84 views

Moment of Inertia of a Motion Simulator Frame

I have a rather specific question. I'm trying to build a motion simulator for flight and racing sims, similar to this: https://www.youtube.com/watch?v=JQAZB3EnI_w . The basic concept is a platform ...
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0answers
19 views

integrating small angular velocities

I know that for a constant angular velocity the following is true: $R=e^{W t} R_0$ where $W$ is an angular velocity tensor, $t$ is a time, and $R$ is a rotation matrix I believe the following is ...
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2answers
105 views

When does angular position, or angular displacement, not obey the rules of vector addition?

The only examples I've found talk about rotating an object about one axis and then about another axis. When you reverse the order, the object ends up in a different position. However, as those ...
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2answers
162 views

Can a quantity have two units?

We know that Force has unit of newton and torque has unit of newton meter. Then if you define the energy, which has same magnitude of work then, $W=Fx$ has unit of Joule ( $J$ ) (or $Nm$ ) while ...
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2answers
1k views

Instantaneous Centre of Rotation

Let's say a body is undergoing both rotational and translational motion. I know that ICR of the body as a whole will be the point about which the body is doing pure rotation, so basically will be the ...
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0answers
57 views

Smallest possible spinning clock?

The earth's rotation acts as a clock and defines a rather precise unit of time called the day. We could go out in outer space and spin a marble and get a reasonable clock. On the other hand, it is my ...
2
votes
1answer
2k views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...