Questions tagged [rotational-dynamics]
A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.
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Does time period of a simple pendulum depends upon the moment of inertia of the Bob of pendulum or its shape?
Time period of simple pendulum is given by
$T=2\pi {\sqrt{\frac{L}{g}}}$
Here L is the length of pendulum i.e. distance between the point of support to the centre of mass of the Bob.
Now consider a ...
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How does normal force act on ring with a point mass on it? [closed]
I have been thinking about this situation, I have no idea how the normal force act of such a body.
Here I have taken the point mass and ring of same mass m but please provide a general solution.
So I ...
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Can u tell whether Acceleration of point contact is correct or not for rolling with slipping (backward slipping)? [closed]
Rolling with slipping backward
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Definition of energy for a Lagrangian with constraints [duplicate]
Suppose I have the Lagrangian in spherical coordinates:
$$\mathcal{L} = T=\frac{1}{2}m (\dot{r}^2 + r^2 \sin^2 \theta \dot{\phi}^2 + r^2 \dot{\theta}^2)$$
Where $T$ is the kinetic energy.
Now suppose ...
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Choice of axis in analysis of gyroscopic precession
In many demonstrations of analysis of gyroscopic precession, the analysis goes on by choosing two axes, one about which angular momentum is calculated, another about which torque of gravity is ...
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Concept of rotational equilibrium [closed]
Consider a rigid square plate of side length 'a' which can rotate freely about the point O in vertical x-y plane as shown in figure. Plate has a groove AB along its diameter. An insect of mass moves ...
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Trajectory of Instantaneous center of rotation of a disc performing both rotational and translational motion [closed]
I am posting the specific problem I am dealing with for reference and then explain the part I am confused with.
My Understanding and approach to the problem
I identified that in the ground frame the ...
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Confusion about torque [duplicate]
Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in ...
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Equation of a bicycle Wheel in free rotation up to stop
I have measured the rotational speed of a bicycle wheel in free rotation up to stop and i would like to have the physical equation (it is not linear). I would like to compute the frictional losses in ...
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Derivative of a curve on a manifold in time-dependent (rotating, comoving) coordinates
This should maybe go in the math SE but the example is more relevant to physics and the way physicists think so I'm posting here.
what I understand: Let $\mathcal{Q}$ be a smooth $n$-dim manifold and $...
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Why consider a rotating ball about a circular track as a point object?
Consider a small ball of mass $m$ translating along a circular track:
As the body reaches the top most part of the circular track, we say that the minimum value of the velocity of the centre of mass ...
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How to calculate total moment around $z$-axis when the armlengths are not the same for all motors on a hexacopter?
I wonder how I can calculate the total moment around $z$-axis at a given rotational velocity for the motors on a hexacopter. My intuition tells me that motors that are more distant to center of mass ...
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Why does a free body rotate about centre of mass when torque is applied? [duplicate]
Suppose a body is kept in space and is not fixed about any point (i.e, not hinged). If an external force is applied, the body rotates about the centre of mass.
I saw one answer pointing out that ...
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Angular velocity in planetary motion
Torque about centre of sun is zero.
$$T=Ia$$
So angular acceleration is zero too, so angular velocity should remain constant.
However it is not the case. Please tell where I went wrong.
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Time Dilation And Comparing Inertial And Non Inertial Reference Frames
Can we calculate the total observed time dilation on a spaceship and a planet by combining the planet's relativistic spin velocity and the spaceship's approach or recession velocity from the planet it ...
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Time Dilation and Spinning Reference Frames
If a spaceship approaches a rapidly spinning planet, would the planet's inhabitants , the inhabitants of the planet where the spaceship came from , and the spaceship's occupants observe time dilation ...
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Reaching 50% the speed of light using a centrifuge
I've seen ideas and previously asked questions for reaching the speed of light through a long bar rotating at some high RPM for the tip to reach $c$. However it seems impossible, so I'm concerned is ...
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Unable to understand the relation between the accelerations of a particle in rotational and inertial frame of reference
I was studying about the derivation of coriolis force and centrifugal force for a particle i.e. the relation between the accelerations of a particle with respect to inertial and uniformly rotating ...
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Axis of rotation of a spool unwinding and falling under gravity
There is a problem that asks for forces that apply torque around the axis of rotation on a spool of string that falls and unwinds under gravity. The spool falls straight down with a vertical string. ...
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Looking for a textbook that covers rotational collisions in depth
I am looking for a textbook that covers rotational collisions. I’m looking to understand “ball-off-wall” collisions. Topics might include reflection, the effects of spin on the ball, and treatment of ...
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If there is an apple vertically above a point on the ground, when it falls from the tree, will it land exactly at that point? [duplicate]
As is well known, when solving the problem of Galileo's free fall (like apples falling from the tree), taking the Earth's surface as a reference frame is considered self-evident. Therefore, if an ...
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How is the angular velocity tensor defined?
Assume we have a position vector $\mathbf r$ dictating the position of a particle in a rotating frame. Then, for a time dependent rotation matrix $\mathbf R(t)\in SO(3)$ that describes the motion of ...
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Which friction acts on on a Rolling body? [closed]
First question is, is it static or kinetic friction which acts on the rolling body or both do?
Say we give a body (sphere lets say with radius $R$) with NO ANGULAR VELOCITY, just linear. Say we ...
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Friction on a rolling body [duplicate]
I have been reading about rolling motion and I seem to have a confusion regarding the friction acting on such bodies.
First off for a body to start rolling their has to be some friction b/w the ...
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The kinetic energy of rotation of a rigid body in generalized coordinates with Einstein notation
The kinetic energy of rotation of a rigid body is given by:
Write T in generalized coordinates in the form:
Determine the explicit form of
I opened the cross product with the civita levi symbol and ...
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If work done by hinge force on a hinged rod is 0, then why is there a hinge force at all?
Consider a rod hinged at one end, and free in the other, initially, the rod makes a 30° angle with the horizontal axis through the hinge, it is then allowed to fall.
I was told, that energy could be ...
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Why is the coefficient of static friction used in the formula for the stopping distance when there is no relative motion between tyres and road?
Instead of using the coefficient of static friction between the tyres and the road, should we not use the coefficient of kinetic friction between the brake pads and the disc?
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Does a force independently affect velocity and angular velocity, or is it split between the two?
I'm implementing physics for a computer game, and came accross something that looks unintuitive to me.
Consider two bodies at rest:
Let's say we momentarily apply the same amount of force to them, ...
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Relationship between tangential and angular acceleration in 3D
In 3D circular motion, $\vec v=\vec \omega \times \vec r$, then the tangential acceleration is
\begin{eqnarray*}
\vec a_t =\frac{d \vec v}{dt} & = & \frac{d}{dt}(\vec \omega \times \vec r)\\
...
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What is meant by angular property wrt body frame?
I keep seeing the phrase "angular velocity with respect to the body frame", or "angular momentum with respect to the body frame" in context of rotation of rigid bodies, especially ...
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Rigid bodies: proof of existence of internal forces that preserve the distances [duplicate]
I am new to Physics and I have a pure Math background. I am currently studying mechanics and I have the following question regarding rigid bodies. I am posting here the 2D version of the question. If ...
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Conservation of angular momentum with no net torque
Suppose there is a point mass with mass m1 orbiting around the z axis at a radial distance r1 with tangential velocity v1. So I would say the angular momentum of this point mass is m1•v1•r1. Then I ...
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Very Basic Question: Calculation of Moment of Inertia Tensor
I am studying from the book Classical Dynamics: A Contemporary Approach by Jose & Saletan, and at page 496, they work through an example about the moment of inertia tensor of a uniform cube
(sorry ...
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Why a spinning top bounces in a direction vertical to the surface that it hits?
When a spinning top slowly advances and hit a surface (a wall), intuitively one would expect that the top gets bounced mostly along the wall, due to the friction between the top and the wall. But the ...
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Energy conservation in Landau-Lifshitz Equation [closed]
considering the Landau-Lifshitz equation for magnetisation dynamics,
$\frac{\vec{M}}{dt}=-\gamma (\vec{M} \times \vec{H})$
In this article (https://arxiv.org/abs/1101.1005), the author argues that $\...
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In which direction does static friction acts on the spool when a force is given to it below centre of mass?
Here, we are provided with a spoolhaving moment of inertia I=kmr², where k is a numerical factor.
I am in the confusion that how should we judge in which direction static friction would be applied,
I ...
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Connecting rotational period with period of oscillation
Recently I have been thinking about if rotational period is somehow related to period of oscillation for SHMs. My original question was how velocity of something impacting a spring affects its ...
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How can you determine if a bar will tilt with 2 points of rotation?
Say we have the typical press machine in the gym to exercise your chest, it is usually helped with 2 points of contact and weights on the sides of the points of contact:
(Sorry for the quality) How ...
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Has anyone tested the Dzhanibekov Effect to see if the frequency of the 180 degree flip changes based on the objects speed or mass?
Rotation around axis 2, the intermediate axis of an object that is not perfectly symmetrical will flip 180 degrees while continuing to spin in the same direction. I'm curious if there is a way to ...
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Why does MOI of rectangle depend on length of diagonal of the rectangle? [closed]
If we have a rectangle of length $a$ and width $b$
my physics textbook showed that the MOI about the axis of rotation in the picture is given by
\begin{align}\label{MOI rectangle}
\dfrac{1}{12}M(a^2+...
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Reason of object not leaving earth surface
The earth rotates around the sun at speed of approximately $18.5$ miles per second. And the escape velocity of earth is $6.96$ miles per second. So the speed of rotation is greater than the escape ...
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Spin and orbital components of angular momentum
From what I have gathered, angular momentum in a system can be calculated about any point. However, I am having trouble grasping this, and below I suggest an imaginary situation where I try to apply ...
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Combination of angular and linear acceleration
I was wondering how the angular and linear acceleration of a body in free fall interacted with each other. Let's imagine a man as a yoyo spinning around a string in free fall. It will have two ...
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Use of Indices while deriving the Inertia Tensor
I'm trying to understand a derivation of the inertia tensor that is carried out for a rigid body rotating instantaneously about a point (the centre of mass):
$$\vec{L}=\int(\vec{r} \times \vec{v})dm=\...
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Why can we conserve angular momentum about the point of contact in rolling motion, even though it's moving itself?
I did find the proof of pseudo torque about the center of mass of a body in combined rotation and translation being zero, and thus I'm convinced that in this frame of reference, we can conserve ...
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Does a vehicle turning on a banked road need to turn its wheels?
A vehicle drives in a circle on a track at constant speed at with radius of curvature $\rho$. The vehicle's acceleration is $$a = \upsilon' T + \kappa (\upsilon)^2 N \\ = \kappa (\upsilon)^2 N.$$
The ...
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Why do spheres indented by a curve follow the curve when later rolled on the same curve?
In this Youtube Short it was mentioned a way of constructing a shape that followings any curve one could draw. Apparently the motivation to construct it is to do the following, roll a sphere of clay ...
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Inertia tensor in canonical and rotated basis
So say we can describe some angular velocity $\boldsymbol{\omega}$ in canonical basis, $\{\mathbf{e}_i\}$, and a rotated basis, $\{\mathbf{\tilde{e}}_i\}$, like
$$\boldsymbol{\omega}=\omega_1\mathbf{e}...
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Is it possible to determine free surface velocity experimentally of the liquid rotating in a cylinder?
Hello Physics StackExchange Team,
I want to know whether it is possible to experimentally determine the velocity at which the free liquid surface is moving/rotating in a cylinder with a rotating disk. ...
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Parallel Axis Theorem Derivation
My professor was deriving the parallel axis theorem wherein he took the Center of mass of an object as some point O and was calculating the moment of inertia about an axis through point P located at a ...
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