**1.671 rotational-dynamics questions.**

According to many rigid body dynamics books, the Euler's equation is expressed in local body frame(principal axes). That is to say the external moment,inertia tensor and angular velocity are all ...

Let's assume a bowling ball is falling to the ground. It will have a certain impact when hitting the ground. Is that impact only depending on the height it's falling from and the weight of the bowling ...

If there is a toy train on the floor moving linearly then would the friction acting be rolling or static?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum:
According to my professor, here we must consider the mass $m$ being in a gravitational ...

Sorry for my broken English.
I am a physics undergrad and only know basic stuff about the subject.
Yesterday I was taught about the angular momentum of yo-yo and
my prof said that when the yo-yo ...

The obvious step is to make the torque due to friction equal to the torque due to tension, so Rf = rT. Then, I decided to get make another equation by assuming that the friction is equal to the cosine ...

In any situation, while applying torque upon any rigid body, can the reference point/axis be any arbitrary point/axis?
I mean, is it necessary for the reference axis to be taken only through the ...

Let's say I have a billiard ball.
Coefficients of friction are known:
μ(rolling) = 0.01
μ(sliding) = 0.2
If we just spin it in place with no velocity.
(angular velocity only have z component, ...

When there are forces acting on a rigid body, the two conditions that has to be satisfied for the body to be in static equilibrium are:
1. The sum of all forces must be zero (translational equilibirum)...

I already know sliding friction of ball on a flat table and rolling resistance of it.
How do I know coefficient of friction value when the ball has backspin with some angular velocity $\omega$? And ...

A man conducted "an experiment" (quotes really, really necessary) to prove that earth is flat. Here's a link. He used a spirit level, set it up before takeoff and expected the level to be tilted after ...

According to Wikipedia to prove $I=I_{cm}+md^2$:
$I_\mathrm{cm} = \int (x^2 + y^2) \, dm.$ $$I = \int
\left[(x + d)^2 + y^2\right] \, dm$$
Expanding the brackets yields
$$I = \int (x^2 +...

I am having some difficulty reconciling what my solution manual says and what I calculating. I would appreciate a peer check on the following.
The problem is described by a stepped cylindrical rod ...

I'm confused about the rotational work, defined as
$W=\int_{\theta_1}^{\theta_2} \tau_z d \theta $
Where $\tau_z$ is the component of the torque parallel to the axis of rotation $z$.
Consider a ...

How is tension in a string able to apply torque on a pulley? How does string itself able to apply a force on pulley? What is happening inside the pulley?
The pulley has a mass $m$ and is a disc.

I'm confused on a scenario. If we roll a ball on a horizontal surface and it rolls without slipping it should eventually stop due to friction. However rolling without slipping means the velocity at ...

Say, I have a system at rest. I was wondering - how many equations of motion can the system have (without redundancy)? Well, I thought that equating the forces along 2 or 3 different axes would give 3 ...

How do I derive Euler's equations of motion for a free rigid body using a Lagrangian formulation?
The required equations are, in vector form, $J\dot{\omega} = -\omega \times J\omega$ where $J$ is ...

I would like to derive Euler's equations of rigid body motion from least action principle.
Suppose we are in free space so we have no gravity so Lagrangian is equal to kinetic energy.
$$
L = T = \...

There are plenty of similar questions here, but I will nevertheless add another one because I believe this is the ultimate source of confusion (and will probably provide a one-stop solution for future ...

We have a 3D periodic crystal and seek to compute the principal axes of inertia. The goal is to have some way to align crystals.
(a) Do the principal axes of inertia exist for a periodic system?
(b) ...

By looking at the rotating car washing brushes, it can be seen that its volume increase with rotation and decrease when it's stopped.
So, just for curiosity, would the earth volume decrease if it ...

So, consider the theoretical situation in which the earth is no longer spinning, and we want to spin it up by running in the opposite direction (Yes, this question was inspired by the Nike commercial)....

I came across this:
If a particle is moving in a circle it is in pure rotational motion about the centre of the circle, while for a moment it may be in pure translational motion about some other ...

This is one of those problems that I thought would be easy, then spent forever on it and realized that I know nothing:
A rigid rod of uniform density has mass $M$ and length $L$ and is free to rotate ...

Can we find the centre of rotation from a free body diagram of a rigid body? Since the forces can be translated anywhere after adding a corresponding torque/couple and this couple can be moved ...

For e.g.
Here, A,B are strings. A was cut. The rod is of length l. Acceleration of center of mass = a and angular acceleration of the rod is alpha.
Now if I want to find the net torque about the ...

Why does the friction of a solid sphere (while rotating and moving) has to be static and not kinetic ,not to slide?

It is well known that rigid body inertia tensors are 3 by 3 positive semidefinite matrices, which is the same as saying that their eigenvalues are all non-negative.
A little less known is the fact ...

I am having some trouble explaining a phenomenon in Newtonian mechanics.
If I have a rigid rectangular rod translating with a constant velocity left to right through space that collides with another, ...

My question is regarding Torque, and specifically the definition of the lever arm.
As far as I've understood, the lever arm is the line perpendicular to the line of action to your reference point.
...

I would like to compute the sum of energy of the following case:
Two solids are turning (disks). Yellow solid is turning at $w_1$ radians per second around its center of gravity and blue solid is ...

Considering a pulley with some mass, or some friction, How can its inertia (or momentum of inertia) influence the tension on 1 rope? Which part of the rope is influenced? Before or after the pulley?

Imagine a rod inclined like a ladder, to the left, touching a wall.
Say, the wall is the Z axis, and the "ladder" is the rod. I want to know how we can calculate the moment of inertia of the rod ...

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight?
I know that its motion depends on the ...

I am trying to find the sound amplitude or level produced by a fan, knowing its RPM.
Is there a simple formula for it?
What other parameters does it depend on? Assume I have all the fan properties, ...

I have been studying Irodov's problem book. There are a lot of good problems that challenge conceptual knowledge, and so I have to ask somebody for a qualitative answer. I can best describe my ...

Why is the velocity different for different points on a rolling wheel?
In the picture which is in the above linked page, I can see the circle which looks like a set of paused points. But I had known ...

Regarding circular motion...
The way that I know of how to derive the centripetal acceleration is based on the geometrical representation of two instantaneous linear velocities of equal magnitudes on ...

Let us imagine some amount of mercury $\left(\text{Hg}\right)$ contained in a cylinder. It is being rotated about the central axis at a constant angular velocity $ω$, and the system has moment of ...

Human beings invented the wheel to get rid of the friction between the wheel and the road. But were we able to reduce it to zero? Is there any residual friction?
This question is about only the ...

As a 8th grader I am still a newbie at science and I have problems understanding the forces that I can not imagine and one of these "forces" is the moment.
We are told that,
$$\text{moment}= Nm$$
...

I'm trying to construct the Lagrangian for the following scenario. A turntable of radius $R$ is rotating at angular velocity $\omega$, maintained by a motor. Two springs with Hooke's constant $k$ are ...

Point A is rotating about an axis with angular velocity
$$w_0=w_i \hat{i} + w_k \hat{k}$$
and has position in the x-z plane
$$r=r_i \hat{i} + r_k \hat{k}$$
In addition, the angular velocity vector ...

Actually I need to rotate the beam (pivoted at centre) with constant angular velocity using the priciple of mass imbalance. Could anyone suggest what would be rate of decrease of mass in one pan (...

Hi: I've read this post: Uniform Circular Motion w/ Tension and Friction and helped me a lot.
I have a similar problem:
At one end of the rope ($R = 1 m$) is tied a mass ($m = 3 kg$) and the ...

In part i, I use $T=I\frac{d^2Q}{dt^2}$ , and get $T=\frac{23g}{150a}\sin Q$ , but the answer is $T=\frac{-23g}{150a}\sin Q$.
The only way I can get this answer is if I use $T=-I\frac{d^2Q}{dt^2}$ , ...

so let's suppose there is a wheel, which rotates thus moving on a flat plane, without any slopes, and the gravitational pull throughout the plane is the same as well. The height of the center of mass ...

A cylinder of mass 5 kg and radius 10 cm is moving on a horizontal surface with velocity of centre of mass 5 m/s towards right and angular speed 10 rad/s (clockwise) . Find the angular momentum of the ...

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