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Questions tagged [rotational-dynamics]

A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

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Are my arms pulled outwards when I sit on a rotating office chair? [duplicate]

Suppose I am sitting in an office chair in a room. Now someone just starts to rotate the chair. The chair is now rotating quite fast. I think my arms will be pulled outwards. Now from my point of ...
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1answer
39 views

Uniform Circular Motion and Work [on hold]

I was usually told that in a uniform circular motion the work is 0 because the force is every instant perpendicular to the displacement. However, studying the motion i noticed that there is a force ...
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13 views

Damping coefficient of cantilever beam under impact load of m and velocity v [on hold]

Critical damping is available but damping coefficient is not available.
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25 views

Find the Angular acceleration of the Roller 1? [on hold]

A heavy plank of mass 100 kg is placed over two cylindrical rollers as shown in figure. Plank is pulled towards right by applying a horizontal force F = 25 N. During the first two second of motion the ...
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43 views

Simulation test for a rotating body [on hold]

I am running a simulation test for a rotating body applying torque to an elastic shaft. For that purpose I am running a simulation for the general equation of motion: $$\tau = I\ddot{\theta}+c\dot{\...
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1answer
49 views

Angular Momentum of Object Accelerating in a Straight Line

I've been given an object with $r(t)=|v|t\hat{x}+b\hat{y}$ and been asked to find the specific angular momentum and see if angular momentum is conserved. I found $L=r\times p=-m|v|b\hat{z}$. My ...
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1answer
33 views

Conceptual doubt in rotation

If a particle is rigidly attached to a ring and the ring is undergoing pure rolling, can I take the the particle to be in pure rotational motion from the view point of the instantaneous axis of ...
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1answer
81 views

Violation of energy conservation during collisions of a particle with different sections of a rod [on hold]

Imagine a homogenous rod with total mass $M$ and length $l$ floating in free space without any force or constraint acting on it. Then, think about two possible scenarios. In the first, a particle with ...
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1answer
62 views

Hamiltonian in rotating frame

I have a Hamiltonian for spin in a magnetic field $$ \hat{H}(t) = \mathbf{B}(t) \cdot \mathbf{\hat{S}}$$ $\mathbf{B}(t) =B_x(t) \hat{\mathbf{x}} + B_y(t)\hat{\mathbf{y}} + B_z(t)\hat{\mathbf{z}}$ is ...
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Rotating particle about the cylinder [closed]

There is fixed vertical cylinder of radius 8cm.One end of thread of length of 1.2m is attached to cylinder and other to a particle which starts moving with constant velocity 6m/s perpendicular to ...
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34 views

Re: Susskind and Hrabovsky: Should the Lagrangian of a particle referred to a rotating frame omit the velocity dependent “potential”?

My question pertains to Lecture 6: Exercise 4 in The Theoretical Minimum by Leonard Susskind and George Hrabovsky. A suggested solution has been posted here: http://www.madscitech.org/tm/slns/ The ...
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Can you tell whether an egg is raw or hardboiled by rolling it down a slope? [duplicate]

Experience books can tell whether an egg is raw or hardboiled by rolling it down a slope. How is this possible and what are you looking for?
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4answers
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Axis of rotation of the body [closed]

A couple is applied to a rod such that the forces are at equal distance from the centre of mass of body. The body will rotate about an axis through its centre of mass. However, if the couple is ...
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0answers
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Components of coriolis force [closed]

$$ \color{black}{ \begin{array}{c|c|c} % START: Column Labels \begin{array}{c} \textbf{Object's} \\ \textbf{direction} \end{array} & \begin{array}{c} \textbf{Horizontal} \\ \textbf{...
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1answer
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Torque of disk about a point when there is a force acting on the disk surface? [closed]

As the picture shows, the force F acts on the solid disk at the contact point $t$. In this case, how do we calculate the net torque about the point $O$, mainly the contribution of F to the net torque. ...
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2answers
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Non-zero torque for a part of rod in equilibrium? [on hold]

Suppose a vertical rod of $L$ length has force $F$ acting towards right, on top and bottom positions. A force $2F$ acts towards left on the centre of rod. The body is equilibrium. Let's take the lower ...
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1answer
27 views

How to resolve impulse on a free-floating body into translation and rotation

I have free-floating in 2D a long thin homogeneous rectangular body with the center of gravity at its geometric center. It seems to me intuitively that if an impulse is applied to the middle of a ...
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2answers
38 views

How is a perpendicular angular momentum origin in gyroscopic precession?

Assume in the given diagram, $\theta = 0$, for sake of simplicity Then, I understand there exists an initial angular momentum in the y-direction and a torque in the X direction of the gyroscope. This ...
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3answers
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Rolling friction and motion [duplicate]

The frictional force in a motion of a rolling body is along the direction of motion. Then what stops the motion of a rolling body?
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0answers
112 views

Why don't escalators slow down when people get on? [migrated]

My friend and I were discussing this earlier: why don't escalators slow down when people get on? We are not interested in any fancy schmancy computers that might adjust their speed for capacity/...
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4answers
75 views

Why does force x distance not equal kinetic energy for objects rolling down an inclined plane?

Imagine two objects at rest at the top of an inclined plane which are capable of rolling and which are identical in every way (mass, radius, etc) with the exception of how their mass is distributed. ...
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1answer
62 views

Is torque always equal to the derivative of potential energy with respect to rotation angle?

For any three-dimensional rigid body, the applied torque on that body is defined as: $\vec{\tau} = \vec{r} \times \vec{F}$ where $\vec{F}$ is the applied force on the object (i.e. $-\vec{\nabla} U$) ...
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1answer
56 views

Conservation of angular momentum during rolling with slipping [on hold]

A block of mass m moves with a velocity $\mathbf{B}$ on a smooth horizontal surface. It then passes over a cylinder $R$ and mass $m$, capable of rotating about it's own axis through $O$. The block ...
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1answer
69 views

Free fall in a centrifugal space ship?

I have read the basics on O'Neil cylinders. A tube with a five mile diameter rotating almost 23 times an hour would produce forces akin to earthlike gravity at the rim. There would be a space in the ...
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1answer
58 views

Work done by moving a body moving on a circular path [closed]

A body moving in circular path of radius $8\sqrt{2}m$ is acted upon by force: $-y\hat i +x\hat j$. Find work done by its complete revolution. So I was trying this question and I could solve it in ...
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2answers
54 views

Net acceleration in circular motion

Why is tangential acceleration of an object moving in circular motion given by $\dfrac{d \vec{v}}{dt}$ I don't know why everywhere it is writen $$\vec{a_{net}}=\dfrac{\vec{v²}}{r} + \dfrac{\vec{dv}}{...
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Why can we use conservation of energy even when friction is involved? [duplicate]

A solid cylinder of mass $m$ and radius $r$ starts rolling down an inclined plane of inclination $\theta$. Friction is enough to prevent slipping. Find the speed of center of mass when its center of ...
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3answers
38 views

Rotor why not opaque?

Helicopter rotors spin at around 300RPM. Now for the naked eye they look like transparent, like if the rotors were not even there. https://www.quora.com/Why-do-we-see-individual-helicopter-rotor-...
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1answer
42 views

Velocity in rotating frame projected onto axis in inertial frame

I want to look at the projection of the velocity of a particle in the rotating frame onto an axis in the inertial frame as a function of time. For example, I am calculating \begin{equation} \frac{d\...
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3answers
69 views

Is it possible to understand the Gyroscope Effect Intuitively?

A stationary wheel, with its axis tied only at one end, falls down, but a rotating wheel, with its axis tied only at one end, doesn't fall down. The explanation given everywhere is by the ...
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2answers
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How to find the axis with minimum moment of inertia?

If a system of particles is given, in a 2D plane, with particles having masses $M_1$, $M_2$, $M_3, \ldots M_n$ and coordinates $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3), \ldots (x_n y_n)$, then how can one ...
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How can an engine provide more torque at the point of contact than the ground's response by static friction without slipping?

In response to the top answer here: Newtonian Mechanics - How does something like a car wheel roll? I clearly fundamentally misunderstand something here. I can't reconcile there being an angular ...
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1answer
34 views

The Euler-Lagrange equations for rigid body rotation

The equations of motion for rigid body rotation are: $I\,\dot{\vec{\omega}}+\vec{\omega}\times I\,\vec{\omega}=\vec{\tau}$ How i can calculate this equations using Lagrangian method ? If i use $...
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2answers
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Moment of inertia rotational mechanics

Moment of inertia of cube about body diagnaol is $ma^2 /6$. Moment of inertia of cube about any axis passing through centre of mass is same only. Is this result correct? If yes how do we prove that $...
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3answers
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Rotation around which axis [closed]

Imagine you have a rigid rod which is free to move and a force is applied at a point away from the center of mass of the rod. This would create torques at multiple points on the rod as the force ...
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1answer
30 views

Rolling point of contact [closed]

I have been reading "variational principles in classical mechanics" by Douglas Cline and the following page rather confused me. It states that for a cylinder rolling without slipping, the velocity of ...
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1answer
55 views

Is there an absence of centrifugal forces in rotating frame of a pulley or in belt friction derivation?

Considering a pulley or belt I understand the derivation of the difference in tension(capstan equation) due the resultant torque needed for the pulley to rotate. My question is for the tiny section ...
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6answers
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If a torque stops a wheel from spinning, will the wheel continue to move forward without spinning?

If a torque applied on a spinning wheel stops a wheel from spinning (on a horizontal surface) will the wheel continue to move forward without spinning?
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2answers
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What is the difference between precession and spin angles?

I was recently introduced to Euler Angles in a Dynamics course, but I am confused on the difference between precession and spin angles. Both precession and spin consist in rotating a coordinate system ...
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1answer
68 views

Kinematic equation for spacecraft using quaternion

I have been trying to find the expression of the quaternion kinematic equation for a satellite in circular orbit in the rotating frame, but I could not find any reference where the derivation was ...
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1answer
72 views

Difference between a point mass and a rotating disk [closed]

In Kinematics, we deal with particles (point masses) which do not have any rotation about their mass centres. In books, it is often mentioned that bodies are analysed as particles but only motion of ...
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3answers
41 views

Why do vehicles with a higher center of mass roll more easily considering that they have a higher moment of inertia?

It is a well known fact that cars with a higher center of mass roll over more easily, but why is this true considering that higher center of mass = higher moment of inertia? I understand that the ...
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2answers
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Torque exercise problem

I am learning physics with help of this site https://www.khanacademy.org/ And I have stumbled upon a task that I can not completely understand The task says: A gasoline engine producing Nm of ...
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1answer
59 views

Linear momentum conservation for interaction between rigid body and point mass

Let's say I have an interaction potential between a rigid body and a point mass expressed in spherical coordinate : $V=V(r,\theta, \phi)$. The coordinates $r, \theta$ and $\phi$ specify the position ...
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1answer
34 views

Equivalent inertia at spherical joint in multibody tree

Consider a tree system of rigid bodies and spherical joints. Starting at an outermost body, I'd like to calculate its equivalent mass (which I'm guessing would be an inertial tensor or something) at ...
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Angular momentum in Rotating Frame for satellites

I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames. To validate my propagator, I am checking the angular momentum and ...
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0answers
34 views

A hemisphere rotating on a flat surface ends up on the flat side. Why?

So I was playing with my kid and this wooden half Kiwi (radius about 20 to 25 mm) got my attention: What I noticed was, when I give it a spin on its pointy end and if a certain initial speed of ...
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0answers
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How does Earth's rotation affect long range shooting trajectory? (Coriolis and Eötvös effects)

I know that this has been a well discussed topic on the internet and I read a lot about it, and yet, I still have some doubts. I'm talking about Coriolis and Eötvös effect. Let's start with Coriolis ...
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1answer
110 views

Rotation matrix help [closed]

So I am doing some exercises in Susan Lea's book Mathematics for Physicists, currently question 7 chapter 1: Find the matrix that represents the transformation obtained by (a) rotating about the x-...
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3answers
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How does a cilinder that rolls without slipping lose energy? [duplicate]

Suppose a cilinder that rolls without slipping on a horizontal rough surface. The slipping is prevented by friction, which therefore slows it down, so it loses kinetic energy. But no dissipative work ...