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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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find rotation points on an object given a center of rotation in other

i have 3 objects, n1 has to rotate from position a to position b, using as pivot point a given one on object 2 (the yellow one). To do that i need to use a 3rd object n3 that can be of the lenght i ...
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Spring oscillation model

When a spring - in real world - is extended $Xo$ from its natural position, it oscillates and eventually decreasing it's amplitude with time, comes to a stop. Is this a damped system or no? If yes how ...
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1answer
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Can we move without moving? [duplicate]

So here is the question, If I jump and hover over the ground for sometime why don't we move away from the point I jumped from? Because earth is rotating so if I hover long enough we should move from ...
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Centrifugal force and centripetal force in fixed coordinate frame

Hello I have a question related to centrifgual force. So in basic textbooks the movement of a particle in a rotating coordinate frame is derived. A starting point is to consider a fixed and a rotating ...
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7answers
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If the mass of the Earth is decreasing by sending debris in space, does its angular momentum also decrease? [duplicate]

We are sending huge amount of debris into space from earth, and also very heavy satellites and rockets, then the mass of earth must be decreasing over time. If the mass will decrease, then ...
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1answer
24 views

Effect of air resistance of the period of a pendulum [duplicate]

Does air resistance increase or decrease the period of a simple pendulum?
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1answer
42 views

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?

Though I solved the question as in the image: Solution: Taking Normal force on aircraft as N. $$\begin{array} {l}{N \cos \theta=m g, \quad N \sin \theta=\frac{m v^2}{R}} \end{array}$$ which gives ...
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3answers
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How can a flywheel make engine run smoothly?

In the video Moment of Inertia Demo, a man states that moment of inertia will be higher if the masses are away from the axis of rotation. The engine take more power to spin the flywheel, because of ...
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1answer
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Conservation of Angular momentum or Work = 0 , which is valid?

In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in ...
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Time taken to start pure rolling rotational mechanics [closed]

The question deals with the basics of rotational mechanics. A cylinder having radius 0.4 m initially rotating at t=0 with angular velocity =54rad/sec is placed on a rough inclined plane making angle ...
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Why does $v\times mv$ vanish in the formula for the moment of force? [closed]

I am currently reading through Goldstein's Classical Mechanics and it defines the moment of force or torque about $O$ as $$N = r \times F$$ and goes through a bunch of calculations to reach $$\frac{...
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1answer
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Nutation frequency for a weighted gyroscope

So, I've been led to believe that the frequency of nutation of a gyroscope can be calculated using the formula In which the I's are the moments of inertia around the principal axes and omega-3 is the ...
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Fixed coordinate frame as limit of rotating coordinate frame

I have a question about a fixed coordinate system as limit of rotating system. Consider for example a pendulum. The Lagrangian in the rotating frame is given by \begin{equation} L(\mathbf{r}, \mathbf{\...
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How to consider a moment of a force as a 2-form?

My major is mechanical engineering. Recently, I'm reading "The Geometry of Physics An Introduction (3ed)" by Theodore Frankel. On page lix in the section O.r, the author discussed the concept of ...
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1answer
43 views

What is the rate at which a precessing top falls over?

From the following equation from hyperphysics, as rotational speed $\omega$ decreases, precession speed $\omega_p$ increases. However, from what we observe physically, as rotational speed of the top ...
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2answers
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Rotating coordinate frame

Hello I have a question about rotating coordinate frames. Following the book of Brizard the Lagrangian is given by \begin{equation} L(\mathbf{r}, \mathbf{\dot{r}}) = \frac{m}{2} \vert \mathbf{\dot{r}} ...
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1answer
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What physical quantity remains equal in different frames? [closed]

I recently came across a problem which involved going into rotating frames. And it was pretty tiring. (And difficult..). So I wondered if there was some quantity that you could measure from the ground ...
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1answer
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Deriving equations of rotational motion for connected rods

I'm working on a problem involving deriving equations of rotational motion for a system of connected rods (see the picture), and I'm a bit confused about a few things to do with rotational motion. I ...
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1answer
76 views

How $ d \vec s = d \vec \theta × \vec r $

Here:- $ d \vec s $ = infinitesimal linear displacement, $ d \vec \theta $ = corresponding infinitesimal angular displacement, $\vec r $ = radius vector I am trying to understand the proof of work ...
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Vertically falling sphere striking a wedge and rolling without slipping

I have a question which states that a sphere of mass $m$ falls vertically and strikes a wedge of mass $M$ and inclination $\alpha$, at rest on a smooth horizontal plane. There is sufficient friction ...
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1answer
29 views

Compound pendulum

Problem: A compound pendulum is formed by suspending a heavy ring from a point on its circumference. Determine the time period of oscillation of radius of the ring is $1\,\mathrm{m} .$ Given that ...
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If there was no friction would a thin rectangle with mass $m$ with sides $a$ and $b$ spin indefinitely about an axis through its diagonal?

I would like a geometrical physics answers so I can have an intuitive grasp about the problem. That means no nonphysical things like matrices, coordinates and random basis of vectors. For example it ...
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1answer
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Does rotation happen throughout the whole x axis of an object simultaneously?

For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion ...
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286 views

Newton's second law in angular form

I'm rather confused about the correct form of Newton's second law in angular form and how matrices of inertia could be converted from one coordinate system to the other. Consider the system below: ...
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2answers
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Conservation of Angular Momentum w.r.t a Reference point

When angular momentum is conserved, does it mean that it does not matter what the reference point is at? Say for example with this image below, the observer stands at two possible points P1 and P2. ...
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1answer
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What is the energy source for Earth movements? [closed]

What is the source of energy responsible for Earth movements (rotation, translation, etc.)?
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Is it possible to find the linear and angular forces?

Suppose an object has both linear an angular motion. Let's consider the object a sphere. What we know: - The angular velocity and acceleration - The linear acceleration of the center of mass. - The ...
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2answers
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What are the ways of applying force axially, without any contact, to a rotating object? [closed]

Is there any other method except just using permanent magnets ? What are the advantages and disadvantages of using the various methods ?
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3answers
398 views

Calculating the moment of inertia of a uniform sphere [closed]

Currently trying to calculate the moment of inertia of a uniform sphere, radius R, I know the answer is $\frac{2}{5}MR^2$ but I keep getting $\frac{1}{5}MR^2$ Setup: Assume mass per unit volume $\...
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2answers
46 views

What is the physics behind a pirouette?

Around last week, I watched a ballet production at the Melbourne Arts Centre, and boy was I amazed! These people dressed up in costumes were spinning on their toes in all kinds of ways, and I was ...
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1answer
34 views

Angular momentum conservation during collision

If I have a disk which is pure rolling and it strikes with a ladder, so can I conserve angular momentum about point O? I think I can because normal reaction passes through O, so torque due to it will ...
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0answers
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Magnitude of moment in 3d space

What's the magnitude of moment about O, if the vectors F, r1 and r2 all lie in the z-y plane? I know the magnitude of the moment is the cross product of force and the perpendicular distance from the ...
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1answer
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Oscillating problems [closed]

I am practicing for my "Mechanics of continuous media" exam. There is two exercises I couldn't really do yet: A homogeneous meter rod at the 70 cm line is hooked up, and making small amplitude ...
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1answer
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Calculating acceleration of end point of rod

Suppose I have a rod hinged at its end, of length $\ell$ free to rotate about an horizontal axis; initially in the horizontal position and I have to calculate the acceleration of its other end point. ...
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Relationship between radius of Euler Disk and radius of path [closed]

Lets say you have a Eulers Disk of radius a which circulates at a circle of radius R with an angle theta from the vertical, what is the minimum possible radius R of the circle in terms of theta and a?...
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1answer
32 views

Waves in rotational motion

If a chain is spun at high speed and let go will that spin on the ground without collapsing, why and how ? If due to a small bump on the road the spinning chain develops a transverse wave what is the ...
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1answer
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How long would “artificial gravity” remain on an O'Neill cylinder without power? [closed]

An O'Neill Cylinder (as defined by O'Neill, per Wikipedia) has two cylinders which are both "5 miles (8.0 km) in diameter and 20 miles (32 km) long, connected at each end by a rod via a bearing system"...
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4answers
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Is the angular momentum in uniform circular motion zero?

In uniform circular motion the direction of linear velocity changes (although magnitude is constant), so linear velocity is not constant and we know that the formula of angular momentum contains ...
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0answers
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Problem with Impure Rolling [closed]

Can someone explain what happens in the below situation Looking at it from the planks frame of reference: The cylinder Velocity= 20(-i) Net friction force on cylinder f=2umg(i) (here u=1/2) ...
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1answer
49 views

Moment of Inertia of Euler's Disc

I was thinking about the Euler's disc and why its angular velocity increases over time. The conclusion I arrived on is that the gravitational potential energy of the disc gets converted to the ...
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1answer
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When considering the torque exerted on one mass by another, is moment of inertia additive?

To be specific: Consider a system with a disk rotating at a constant speed and a disk hovering above it, not rotating. When the hovering disk is dropped on to the rotating disk, we want to know the ...
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Factors effecting the time period of Euler's disk [closed]

I wish to carry out research on the factors effecting the time period of a spinning Euler's disk. Do factors like friction coefficient of the base or concavity of the base effect the disk? If not, ...
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1answer
45 views

What are the forces acting on this car?

i found a cool website that explains sort of like the forces acting on the car and they seem to explain the process behind it. the website gives a free body diagram but the problem is that it doesn't ...
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1answer
22 views

Parallel axis theorem of stick-ball configuration

I have a system with a rod of mass m and length 2a. Let the origin be in the middle of the rod at x = 0. (Therefore, each end is a distance a away.) A ball of mass m is attached to the far right end. ...
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Understanding the rate of change of linear and angular momenta

I was refreshing my memory on Newtonian mechanics, and I ran across Torque in a non-inertial frame. I worked out the derivations for the rate of change of linear and angular momenta starting with the ...
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Why does the parallel axis theorem apply in this case?

Next, the wheel is flipped over, so the angular momentum of the wheel is now negative. Obviously, the person must start rotating counterclockwise to conserve angular momentum. Since the person is ...
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2answers
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Is the parallel axis theorem valid for non-rigid bodies?

For some context, consider an idealized situation with a person, rigidly attached to the shaft of a bicycle wheel that can spin. sitting on a chair that can rotate. All bearings are frictionless. ...
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2answers
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What's causes the 'backspin' while sliding a pencil along a table? [duplicate]

I've always thought it was weird that pencils act like this: if one pulls their finger along the side of a pencil until it touches the surface below, the pencil is launched in the opposite direction ...
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Newton's second law in non inertial frames: why am I getting $r_x = 0$?

Consider the following system: and the following frame: A rotating frame $x^{\prime} y^{\prime} z^{\prime}$ whose origin coincides with the inertial frame $x y z$ and the $z^{\prime}$ and $z$ ...