Questions tagged [rotational-dynamics]
A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.
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Rotational motion and angular momentum ABOUT centre of mass
Note- By COM i mean the Centre of mass.
What i have been thaught about the net angular momentum of a system is that -
$$\vec{L}_{Net}=\vec{L}_{ of COM}+\vec{L}_{About COM}$$
Now here the $$\vec{L}_{ ...
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Conservation of Angular Momentum, why does person rotate only one way?
As seen from the video that i linked, when the wheel is spinning then he doesnt rotate, but as soon as he flips the wheel he will start to rotate. Why he doesn't rotate both counter and anticlock wise?...
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Equation of Motion of Rigid Body Represented by Twist and Derivative of Twist
This question is an extension of question Understanding terms Twist and Wrench.
Assuming there is a rigid body with body twist denoted as $\mathcal{V}_{b}=\left(\boldsymbol \omega_{b}, \boldsymbol v_{...
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Confusion regarding SI-units of Stiffness $K$ [duplicate]
I know that stiffness,$K$ is equal to product of moment of inertia and square of the natural frequency
$$ K=J\omega_n{}^2$$
Where $K$ = stiffness, $J$ = moment of inertia and $\omega_n$ = natural ...
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How does a linear momentum transfer to angular momentum?
What if i have a system consisting a rod with 2 balls with same mass at both of the end, if a third ball fall into one of the balls on the rod with a speed $v$ and mass $m$, suppose the third ball ...
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How can an object have more than 3 degrees of freedom?
In 1 of my robotics classes our professor told us that something can have up to 6 degrees of freedom:translation in the x axis , translation in the y axis,translation in the z axis,rotation around the ...
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How a particle moving in an straight line is perceived in a rotating frame of reference?
Imagine two reference frames that share same origin. One is static (S frame) and the other one is rotating (S' frame) with $\mathbf \Omega = \Omega_0 \mathbf k$. Imagine we throw a ball in an straigth ...
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Problem with Center of mass equation definition
I was trying to motivate the definition for the center of mass formula and I am getting a weird result. For simplicity let's assume two-point masses of mass $m$ and $2m$ connected by a rigid massless ...
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Even considering angular momentum conservation, is Newtonian mechanics the same as Lagrange mechanics? [duplicate]
I heard that Lagrange mechanics can be derived from Newtonian mechanics, and Newtonian mechanics can be derived from Lagrange mechanics. I've heard many times that they have equal explanatory power. ...
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How do I write angular displacment in quaternion form? [closed]
Work done is given by $W = F_ids_i$ and in angular displacement moment form it is $W = \tau_i d\theta_i$.
I want to get the work done in using quaternion instead.
Like
$W = \tau_i q_i$
I cannot figure ...
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Work done by friction in pure rolling
I just want a clarity about work done by friction in pure rolling when external force is acting. So suppose we have a ring and an external force is applied at the centre, the ground has friction. ...
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Rolling and slipping [closed]
If a rigid disc purely rolls over a very rough surface before suddenly entering a slightly less rough surface would it slip?
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How to derive moment of inertia for a thin disc?
Wikipedia's article on moment of inertia provides examples of how to derive the moments of inertia for different bodies:
$$I_P=\iiint_Q p(x,y,z)||\mathbf{r}||^2 dV$$
It gives an example of how to ...
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Does rod in free space rotate around CoM if continuous force act at one end?
This site has lots of similar questions like mine, there is force just instant strike after that object moves freely, so my question is not like these.
Rocket engine produce continuous force at one ...
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Centripetal acceleration and tangential velocity for object that rotate and revolve in same time?
Right picture is two turn tables on of top of the other, smaller turn table is connected with shaft to bigger one so it rotate around itself and in same time "revolve" around center of ...
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How bicycles automatically steer into the fall - have we been using the wrong physics in trying to explain it? [closed]
There are many posts/questions discussing the physics of a bicycle front wheel. The ones trying to understand the self-turning motion all try to find where the torque comes from that turns the wheel. ...
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Angular motion in collisions
In general, knowing the mass distribution of two colliding objects and the exact point of contact, how would one take into account angular motion in the analysis of the dynamics of the individual ...
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Angular Acceleration about stationary point in pure rolling
I was reading David Morin's "Introduction to classical mechanics ", Chapter Angular Momentum Part I, where I found this paragraph. " Invariably, we will calculate angular momentum and ...
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From where does static friction transfer energy, in case of a car?
Let’s take the scenario of a truck which has a block kept on it and it starts to go around in a circular path. It stops later after one circle, at it's initial position. If we consider the journey of ...
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Weird rotational movement of a cylinder
I have had this question for a while. Let's suppose we have a disk/cylinder with a radius $R$ and mass $M$ placed along its length on a flat surface. We press one of its sides with enough force, and ...
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Why does the bottom most point in pure rolling has zero tangential acceleration?
In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be ...
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Is Torque always defined about the axis of rotation?
My professor told me torque can be calculated about any point in space, but would such a torque ever make sense even if the particle is rotating about some other axis, on which the point does not lie?
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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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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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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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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 ...