**1.724 rotational-dynamics questions.**

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 ...

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 ...

I understand when a force is applied to a body it causes moments on all points not lying on the force's line of action. So which of these points acts as the pivot point around which the body actually ...

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 ...

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 ...

I am aware of spaghettification effect caused by entering a black hole, as well as fundamental physics of an object in space, so here is my theoretical construct:
if I place an object in space where ...

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 ...

I saw this mind boggling result that if the tires don't slip then the work done by an engine to move a car is zero. Why is this true? Moreover, what does this truly mean?
Update: Sorry about not ...

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-...

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 ...

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 ...

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 ...

Is it possible to calculate rpm of a gyroscope based on the mass of a gyroscope and the force that acted on it? Let say the mass of the gyroscope is 1 kg, and the force is 5 torque. Is there any ...

The answer is C.
I'm thoroughly confused! The question is asking for when the magnitude of the vertical component of the force that the wall exerts on the left end of the beam is the smallest. How ...

Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...

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.
...

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 ...

When a ball rolling without slipping along an inclined plane reaches the bottom, it has a linear velocity $v$ and angular velocity $\omega\ =v/r$ at the bottom. Then it continues its motion on the ...

In a welcome triumph of technology, Canada shoots its three federal party leaders far into space.Scheeridan, TrustDuh, and SingASong have identical masses of 80.0 kg and they are tied together with ...

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 ...

Let's suppose I have a ring of mass m, and radii r, thickness t, and width w, as shown:
I would like to come up with a way to be able to work out the highest RPM a ring can reach given m, r, t and w, ...

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 ...

I am a high school student. I am having confusions about the centripetal force and rotational motion.
I have known that a body will be in rest or in uniform velocity if any force is not applied. But ...

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 ...

Say I got a so massive rod and a relatively light spinning flywheel. Fixing an end on a pivot, and the disk on the other endpoint, as expected, the rod would undergo precession.
If we call the plane ...

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 ...

Angular momentum is always calculated about an axis and not about a point( according to me).
I have a scenario on this topic. In the image below it is asked to calculate angular momentum about origin....

According to this article, a Foucault pendulum proved Earth was rotating. I'm not sure it really proved it.
If Earth weren't rotating and a Foucault pendulum started in a state with zero velocity, it ...

Let's consider the classical example, the wheel hung by one side of the axle:
¹
When the wheel is not spinning, it will tilt down the free end of the axle first.
When the wheel is spinning, it will ...

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 ...

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 ...

I would like to calculate the angular acceleration of an object on which a force $F$ is applied at point $P$. The scene is 2D, and the complex object consists of many axis-aligned rectangles.
I ...

I'm learning physics on Khan academy and i have stumbled upon a task that I cant completely understand and I'm a type of person that cant continue the studying until everything that I have read is ...

I'm faceing a problem of a thin wheel of radius R rolling without slipping on a track (y = f(x); on xy-plan). The wheel plane stays vertical and tangent to the track at the contact point P. $\alpha$ ...

In the classic example of gyroscopic precession, the wheel starts to process, and now acquires a angular moment also in the vertical direction. Initial angular momentum was in a single plane. The one ...

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 ...

I'm trying to solve for the rotational motion of a rigid body in the absence of external torques using quaternions in MATLAB. Assuming the axis of rotation as the unit vector $\begin{bmatrix}a_x & ...

I'm supposed to find the angular velocity of the uniform rod (mass $m$ and length $L$) when a constant, horizontal force is applied at the bottom using work-energy theorem.
I tried to solve the ...

If the distribution of mass in a shaft is such that it is balanced around its center, then the shaft may still generate a couple force if the weight is not balanced around its axis of rotation. For ...

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 ...

Is the angular velocity of a rigid body about any point the same as that about the axis of rotation. Also, can we even define angular terms (Angular Velocity, Angular Acceleration, etc) about any axis,...

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 (...

If you turn the front wheels of a car you get cornering forces at the wheels. At the next instant you still have cornering forces without turning the wheels. Aren’t the wheels still turning (i.e. ...

In class we are looking at rotation about a fixed axis. Using the n-t coordinate system, the notes derive the acceleration like:
(1) $a= \frac{dv}{dt} = \frac{d\omega}{dt}{\bf{r_p}} + \omega\frac{d{\...

Define the action
$$S[g]=\displaystyle\frac{1}{2}\int^1_0 Tr(I(g^{-1}\dot g)~g^{-1}\dot g)~dt.$$
$I:SO(N)\to SO(N)$ denotes the endomorphism $\omega \to I(\omega)$ with $I(\omega)_{ij}=\omega_{ij}/...

Sorry for boring you during summer vacation, my friends. I am haunted by the comparison between Euler angles and Rodrigues rotation formula under the small rotation hypothesis. Maybe, they cannot be ...

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