Questions tagged [rotational-dynamics]

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

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Trouble implementing transfer function of a wheel driving force observer

I'm trying to implement a piece of software that can determine Fd(the driving force of a wheel, shown in figure below) given w(angular vel), Tm(wheel torque) and r(wheel radius). What I don't ...
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1answer
66 views

Will a rotating disk contraction emit light?

The Ehrenfest paradox suggests an object will become smaller at the outer rim due to contraction, When near light speed. Or actually, any object near light speed will contact and appear smaller in its ...
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Lagrangian mechanics a cylinder on a cylinder barrel

This is a typical problem to be solved using the Lagrangian mechanics, but I have a problem in understanding the rotational energy. The task is to formulate the Lagrangian equation for the system of ...
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39 views

Interesting classical mechanics question! Any ideas? Yo-yo in space [on hold]

Imagine a cord wrapped around a wheel in free space (essentially a Yo-Yo). In a frame that is moving with the wheel, what happens to the cord and the wheel when the cord is pulled from 0 velocity to (...
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1answer
17 views

Tangential velocity after ball strikes wall

I have to solve a problem where there is a ball that goes in the perpendicular direction towards a wall. It strikes the wall and goes back at the same angle it came from. (All the movement are ...
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4answers
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Angular momentum and torque in gyroscope

In my textbook (Kleppner), the principle of a gyrocompass is given to be "A flywheel free to rotate about two perpendicular axes tends to orient its spin axis parallel to the axis of rotation of the ...
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What is the moment of inertia for two identical masses that lies not symmetrical to each other INSIDE a cylinder? [on hold]

Suppose I have a cylinder with r = 5.2cm, two masses are both ~200g, radius of the mass is 2cm each. If both of them are on the same line as the diameter of the cylinder (mass 1, center of cylinder ...
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Derivation of the time-derivative in a rotating frame of refrence

I have so trouble following Goldsteins derivation of the time derivative in the rotating refrence frame, and its use to derive the coriolis force (sec. 4.9-10) Given an intertial frame of refrence, $S$...
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Principal axes of cube at one of it's corner [on hold]

Find the equation of momental ellipsoid at the corner of a cube of side $2a$ referred to its principal axes. I have specific doubts in this question. At any point, angle which the principal axes ...
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1answer
49 views

Whats wrong in the torque method to get the time period for a semi cylindrical shell? [on hold]

Problem is : My all working is shown here : using 1 and 2 i am getting it to be 2pi√2R/g using energy equation it will lead us to correct answer but why the torque method is not working? Here A is ...
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Time taken by a round object inside rotating cylinder to exit from a hole

I want to know the time taken by a round object of sphericity of 0.85 inside a rotating cylinder to exit from a hole. The below figure will explain my query in a simple way. The notable points are: 1. ...
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Euler's Equation of Motion by Lagrange's Equations [duplicate]

currently i am studying three dimensional rigid body dynamics. My question is how to derrive the popular Euler's Equation of motion given by: $\sum M_x = J_x\dot{w}_x-(J_z-J_y)\omega_y \omega_z $ $\...
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Difference b/w axis used in angular momentum and conservation of angular momentum

We study that $L= L_{spin} + L_{orbital}$ where the $L_{spin}$ is always calculated about the $CM$ of the concerned body . But what I dont understand is thay when we apply conservation of angular ...
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1answer
76 views

Rotational motion integration (Rigid body dynamics)

I am trying to integrate the rotational motion of a rigid body (a set of N point masses) $\textbf{in the inertial frame}$, but my results seem totally wrong. What of the following steps could be wrong?...
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1answer
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Rotation of top of symmetries

while learning about rotation, I started to wonder what forces will come into play. Lets picture a top with two masses centered at (-1,0,-1) and (1,0,1) with rods connecting the masses directly to the ...
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1answer
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The units when calculating Gyroscopic precession rate don't make sense [on hold]

I was doing a problem set for my physics course and I ran into some odd units for calcualting the gryeoscopic precession rate. As it is the angular velocity of the wheel around the axis, it should be ...
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1answer
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Does direction of angular velocity/acceleration have any physical implications?

when first learning about the angular velocity/acceleration, the right hand rule is mentioned. According to it, the direction of angular velocity/acceleration is along the axis perpendicular to the ...
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Friction on the surface of a pulley

1)Is friction between the part of string in contact with the pulley and the pulley same throughout the entire surface of contact ? 2)what is the linear work done by this friction when the pulley ...
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2answers
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Rotational Work done by Friction

(Okay so I have asked this in a previous post but I think this should be a separate question) Consider a cylinder performing accelerated pure rolling (Static friction is non-zero) on a sufficiently ...
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3answers
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How can you predict whether an object is going to rotate? (question about torque)

I know a torque causes angular acceleration, but the derivation for the formula $\tau = I \alpha$ seems to assume the object is going to rotate in the first place, as it uses the identity $a_{tan} = R ...
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1answer
25 views

How to calculate inertia tensor of composite shape with angle? [duplicate]

I have I have some objects assembled like this : The inertia tensor would be : $$I=I_1+I_2+I_3-m_1 \,\tilde{r}_{01}\,\tilde{r}_{01}-m_3\,\,\tilde{r}_{03}\,\tilde{r}_{03}$$ Where : $$\tilde{r}_{01}...
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1answer
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Doubt in cylinder going up a step at constant angular speed

I have this problem here: I think I know how to solve everything except for the number 2). I studied in the mechanics subject that $W_{ext}=K_{2}-K_{1}$. Where $W_{ext}$ is the external forces' work ...
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1answer
39 views

Intuitive understanding of angular momentum in cartesian coordinates

If a point-mass body is moving in a plane $z=0$, its angular momentum can be taken to be a scalar, and from the vector product formulas (assuming $m=1$ as I'm only interested in geometry), its value ...
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4answers
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Kinetic Energy of a spring cylinder system

Consider the system in the above diagram. The surface has enough friction to initiate pure rolling. Questions: 1)If we stretch the spring from the equilibrium by about some distance x. The spring ...
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1answer
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How to calculate inertia tensor of composite shape?

How can I calculate inertia tensor of composite shape. I have done math of moment of inertia, but not inertia tensor. Can anyone help me with the calculation of this shape :
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Confusion about torque and net force

This is a question I was trying to solve: A uniform disk of mass 1 kg and radius 1 m is kept on a rough horizontal surface. Two forces of magnitudes 2 N and 4 N have been applied on the disk as shown ...
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3answers
63 views

Finding angular momentum in a special case

Let us say there is a rigid body M which is rotating about an axis which is not passing with an angular velocity $\omega$ through it's centre of mass and simultaneously translating with a velocity $v$....
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1answer
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Heat produced if earth stops rotating

In my textbook there is a question that is as follows:- If earth stops rotating about it's own axis,the increase in its temprature will be(Here R=radius of earth,ω=angular velocity of earth,J=...
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2answers
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Do internal forces always act along the line joining the particles?

For the rate of change of angular momentum of a system to be equal to the torque due to external forces, the torque due to internal forces should be zero. This will mathematically be possible only ...
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1answer
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Direction of friction in pure rolling

Suppose a disc or a sphere with uniform mass density is purely rolling without any slipping/sliding on a ground having friction. Will there be friction acting on the disc/sphere? If yes, what will be ...
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Pure rolling on accelerated plank

A sphere at rest is placed on a plank. After that plank starts accelerating. My doubt is that what is the direction of motion of sphere when the plank starts accelerating to the right? It is given ...
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4answers
51 views

Doubt relating pure rolling

As we know, when an object perform pure rolling on a plane having friction the friction acts on the edge in the direction opposite to the direction of its translational motion. There are no other ...
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4answers
71 views

Is the Earth a gyro?

Due to rotation and low friction, can the Earth be considered a gyroscope? If so, any interesting implications to this? Thanks
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Collision of Rolling body

When a rolling body collides with a wall elastically,its torque is zero.But direction of velocity of particle is reversed.So will the angular momentum be conserved?
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The confusing Wikipedia article about Euler's equation of rotation

Here is an article from Wikipedia on Euler's equations. In the derivation of those equations, I find the torque $\mathbf M$ quite confusing. There are two torques there -- $\mathbf M$ and $\mathbf M_{...
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1answer
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Does a “gimbal hinge” have the same degrees of freedom as a ball-and-socket joint?

I am trying to design a joint to 3D print and considering different models. One model was a traditional spherical ball-and-socket joint. However, due to production issues, I am considering other ...
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Force balance with different points from centre of rotation

Problem is as shown in the image above. The shape made of black lines is a rigid body. The input force of 100N is exerted on point 1; this causes torque of 100N.m at the rotation point. What is ...
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1answer
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Transforming inertia tensor from corner of a beam to the centre [closed]

So I have a beam with mass M and sides a (x-direction) ,b (y-direction) and c (z-direction). I have figured out that the inertia tensor in the corner is $$I = M\begin{bmatrix} \frac{b^2 + c^2}{3} &...
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1answer
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Magnus Effect influencing Hurricane Balls motion?

In the motion of a hurricane ball, two sphere are glued or welded to each other and can be spun at very high RPM's, while one ball is rotating on a surface, the other ball is inclined to the surface ...
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Degree of freedom in ideal and real case

what will be the degree of freedom of a massless rod, moving freely in space with a particle which is constrained to move on it? What is meaning of massless rod?
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2answers
81 views

Rotating rope with a ring

I have this ideal system. There is a bar with negligible mass and a ring(a point) with mass $m$. Bar is rotating with angular speed $\omega$. If I see that system from Non-inertial reference system I ...
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2answers
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Why do tensions cancel out in some places but not others?

I was answering a question regarding two rotating particles $P$ and $Q$ with $P$ attached to a fixed point $O$ by a light inextensible string and $Q$ attached to $P$ by a light inextensible string ...
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1answer
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Why people feel outward force in rotor ride?

I know centrifugal is fictious force but what is possible reason for the force that people feel in rotor ride outwards. The reason for people not falling down is friction force which is in vertical ...
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Equilibrium of a rotating particle

Consider a point like particle rotating in a circle with constant angular velocity. Then there must be a centripetal force ok, now the question is can we say that object in equiliibrium? If your ...
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1answer
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How can I calculate the internal angular acceleration? [closed]

This is a very well known topic and affects angular velocity. How does changing the moment of inertia affect angular velocity? An object that changes the moment of inertia simultaneously changes the ...
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2answers
81 views

Hollow cylinder with ball inside rolls down frictionless inclined plane [closed]

I have an question about rotational motion of the following system There is a hollow symmetric cylinder on a friction-less inclined plane (mass M, moment of inertia I, radius R, incline angle a). We ...
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1answer
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Will the rods rotate about the hinge after collision?

The problem is like this: two blocks(considered to be point masses) of masses $m$ are simultaneously moving with uniform velocities $v_0$ towards the rods and they hit the edges of rod and stick to it(...
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139 views

What makes a forever spin top special?

What is the difference between a regular spin top and a forever spin top (which spins for far longer than a regular spin top).? The forever spin top is made out of stainless steel. I would like an ...
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1answer
68 views

Friction as a cause of motion

Can anyone help me to understand why friction force is not opposing the resultant centripetal force acting on the box and instead being the cause of its existence?
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How does vibration transform after rotation of the vibrating object?

I can't find the math of that. Imagine a vibrating object, like a circular membrane, with vibration modes $\phi_{ij}(x,y)$. Let's express the initial vibration state like $u(x,y,t)=\sum_{ij}a_{ij}e^...