The time derivative of angular position used when studying rotating objects or systems.

learn more… | top users | synonyms

2
votes
0answers
48 views

Rotation of rod [on hold]

A uniform rod of length "L" is free to move and rotate in gravity-free space . when an impulse is given to one end of the rod perpendicular to its length, its center of mass moves with velocity "V". ...
2
votes
2answers
274 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why? Please try to give a different explanation ...
3
votes
1answer
637 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
0
votes
0answers
11 views

Determining velocity and angular velocity after a collision between two 2D rectangles [closed]

Say I have two rectangles, which each have four vectors (which represent their vertices), a velocity, a mass, an angular velocity and a rotation (which is only used to simplify calculations as I don't ...
-2
votes
0answers
32 views

Rolling Coin (Old Physics Quals Exam) derivation help [duplicate]

I am trying to understand the derivation for the angular velocity of a rolling coin in the problem given on this website: http://functionspace.com/question/27/answer/121 How does one find angular ...
4
votes
1answer
554 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 ...
1
vote
2answers
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 ...
0
votes
1answer
54 views

Does adding mass to the fan blades affect its max velocity?

If I replaced fan blades with congruent blades, the only difference being the second set has a higher density, would that affect the speed cap on the spin? I know it would affect acceleration, but I ...
1
vote
1answer
51 views

torque needed to precess the angle of rotation

If a rigid body with the inertia matrix $I_B$, has the angular velocity $\overrightarrow{\omega_1}$ what torque is needed to rotate it around another axis say $\overrightarrow{\omega_2}$ while keeping ...
1
vote
0answers
37 views

Is there a limit in angular speed in special relativity? [duplicate]

I was thinking in the following problem: Suppose I have a bar of lenght $l$. If I spin it with constant angular velocity $\omega$, according to the special theory of relativity, is there a limit ...
0
votes
1answer
282 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
0
votes
2answers
272 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 ...
0
votes
1answer
120 views

Angular velocity of disc from induced motion

I came across a question regarding linear momentum $L$ and it's conservation, however I tried and got confused. It reads: A $40kg$ girl stands on the very edge of a rotating disc of mass $50kg$ and ...
11
votes
7answers
2k views

Does cutting of trees affect spin angular momentum of earth?

Cutting trees reduces earth's moment of inertia. So the spinning velocity of earth should be reduced day by day. Does it really happen?
1
vote
2answers
17k views

Calculation of the G-force

I have a formula which is $\text{G-force} = \frac{v\omega}{9.8}$, where $v$ is speed and $\omega$ is the angular velocity. I've seen on the internet that G-force is actually $\text{acceleration}/9.8$. ...
0
votes
1answer
43 views

Predicting top speed of a flywheel [duplicate]

I connect a DC motor to a flywheel with a given moment of inertia. I then supply that motor with a constant voltage and current for an infinite time interval. What do I need to know about my motor to ...
3
votes
1answer
58 views

Is there an angular velocity operator in quantum mechanics?

In classical mechanics we can write as velocity of a rotating object $\vec{v} = \vec{\omega} \times \vec{r} $ or in analogy the momentum $\vec{p} = m (\vec{\omega} \times \vec{r})$ using the angular ...
2
votes
5answers
388 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm $OA$. ...
1
vote
1answer
390 views

Magnitude of the average velocity vector (not the average speed)

Thank you ahead of time for taking to look at this. For this following problem we were given an answer however I am almost positive the given answer is wrong. It doesn't even make sense. So here is ...
1
vote
2answers
628 views

Too big to revolve like an atom? [closed]

At what point do objects naturally start revolving as a disk? From an atom, with which the electron revolves as a sphere, to a galaxy, that revolves in the same direction? I herd about rigid ...
0
votes
1answer
38 views

Acceleration in full-swing pendulum

Consider a $360^{0}$ swing pendulum with a massless rod. If I start it from the position of unstable balance, at the very top of the circumference, according to the conservation of energy, its ...
1
vote
2answers
126 views

Special Relativity - oscillator paradox

I am reading about the Special relativity and the original Einstein papers from 1905 and 1920 where he derives the Lorentz transformation and the effects of the time dilation and space contraction ...
0
votes
0answers
22 views

What is the exact physics behind the heading indicator?

If I know right, the really basics of its functioning is that a quickly rotating gyroscope's axis of rotation moves into the north-south direction, due to the torque resulting from the tangential ...
0
votes
1answer
26 views

What are the Radial, Tangential and Linear Velocities in this Context?

From the pictures below, it has been said that the tangential component (represented by the tangent at $B$) the linear velocity of a particle moving from $A$ to $B$ is $r \omega$, which is equal to ...
1
vote
2answers
53 views

How do I find the linear components of acceleration in a pendulum?

I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
-1
votes
1answer
65 views

Why is angular acceleration of a pendulum always negative?

I was trying to derive using the Lagrangian the equations of motion of a simple pendulum under the influence of gravity. Eventually, I was brought to this conclusion: $$\alpha = -(g\sinθ)/l$$ where $\...
0
votes
1answer
32 views

Why do we represent the axis of rotation using vectorial notation [closed]

When a body (in pure rotation) rotates along an axis passing through it, why do we represent the axis of rotation in vectorial notation? Wouldn't it be sensible enough to represent the angular ...
0
votes
1answer
34 views

Rotation and Momentum

I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector. However, is it correct ...
0
votes
2answers
170 views

What is the dimensional formula of angular velocity?

I have problem to determine the dimensional formula of angular velocity. My friend said that the dimensional formula of angular velocity is $T^{-1}$. It's come from rad/s, rad is dimensionless, the ...
5
votes
3answers
10k 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 ...
0
votes
2answers
31 views

Velocity of the points of a rigid body

The most general motion of a rigid body is a roto-traslation. Firstly is it correct that any point (let's call it $O$) of the rigid body can be seen as the point through which passes a istantaneous ...
-3
votes
1answer
45 views

Lagrangian in polar coordinates [closed]

$$L=\frac{1}{2}mv^2=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)$$ $$L=\frac{1}{2}mv^2=\frac{1}{2}m(\dot{r}^2+r^2\dot{φ}^2)$$ I dont get this part. $$\frac{d}{dt}\left(\frac{\partial{L}}{\partial{\dot{φ}}}\...
2
votes
1answer
111 views
0
votes
2answers
36 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
1
vote
2answers
103 views

Centripetal force: if radius decreases, does ANGULAR or TANGENTIAL velocity change?

Having conceptual trouble with this aspect of centripetal force. Say we have a puck on a frictionless table attached to a string that I am holding through a small hole, so that the puck moves in a ...
0
votes
1answer
74 views

What is $\omega \times v$?

I found that equation in my textbook. It says that $\omega \times v$ ($v$ is velocity) is centripetal acceleration. But how is the equation derived?
1
vote
2answers
81 views

Angular momentum of rolling sphere [closed]

A sphere of uniform density $\rho$ and radius $r$ is rolling without slipping on a perfectly flat surface. It is moving in a perfectly straight line and its axis of rotation is parallel to the plane ...
0
votes
2answers
36 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...
0
votes
3answers
86 views

Rotation of rigid body with two different angular velocities

Consider a cylinder that rotates about a vertical fixed axis with angular velocity $\vec{\Omega}$ while rotating about a vertical axis passing through its center of mass with angular velocity $\vec{\...
1
vote
1answer
21 views

Angular velocity and velocity of CM indipendence in rigid body motion

In the most general case, in rigid body motion the linear velocity of the center of mass $v_{cm}$ and the angular velocity of the rigid body $\Omega$ are not related with each other. Which condition ...
0
votes
2answers
44 views

Proof derivative of a vector following precession motion

I do not get some points of this proof about the time derivative of a unit vector $\hat{u}$ (costant magnitude) which is following a precession motion. The picture is the following. I want to ...
0
votes
0answers
63 views

Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\...
4
votes
2answers
5k views

Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
2
votes
1answer
37 views

Component of angular momentum perpendicular to the rotation axis in rigid body rotation

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation $...
0
votes
1answer
36 views

Proof of constant angular velocity in rigid body motion

I'm studying rigid body motion on Landau but I'm having troubles to understand this proof of the fact that the angular velocity $\vec{\Omega}$ is constant for a rigid body. My doubt is about the ...
1
vote
1answer
50 views

Why will kinetic energy decrease?

Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ...
0
votes
1answer
48 views

How does angular velocity transform on the surface of a sphere?

If we consider the earth as a sphere than it will have an angular velocity of $\boldsymbol{\omega}=\omega\mathbf{e}_z=\frac{2\pi}{T}\mathbf{e}_z$ where $T\approx24h$. Now we have given a location in ...
15
votes
3answers
8k views

Home experiments to measure the RPM of a pedestal fan without special equipment?

Is it possible to determine to an approximate degree, the revolutions per minute of a fan, for example a pedesal fan pictured below, without using some electronic/mechanical measuring device? One ...
0
votes
2answers
72 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
0
votes
0answers
50 views

Converting torque to angular velocity

Given the torque of a system, is it possible to convert this torque to the angular velocity of the object? I calculated the torque exerted by wind on a blade, however, now I need the RPM. To get the ...