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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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Why is the moment of inertia the rotational analog for mass and not inertia?

I've thought that both mass and the moment of inertia measure an object's inertia, one being in translational motion and the other in rotational motion. That has made complete sense to me, but in my ...
Hani Ismael's user avatar
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3 answers
22 views

Would a homogeneous rod on a fulcrum oscillate or remain at rest after displacement?

If I take a homogeneous rod, put it on a fulcrum, push one side down in a controlled way and release very carefully won't the rod just stay at rest in that new position? ChatGPT says that it would ...
Matthias's user avatar
1 vote
3 answers
74 views

Conservation of linear vs. angular momentum in two similar cases

I have a question that eludes my understanding: Imagine we have a bullet of mass $m$ and a rigid pendulum with a bob of mass $M$ hanging from a rigid rod of negligible mass hanging from the ceiling ...
Giovanni Piacentini's user avatar
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0 answers
32 views

Two cylinders rolling without slipping on planks

I am struggling with the following setup. This setup consists of three massless planks and two massive cylinders, as can be seen from the figure. The lower plank is pulled with a force $F$ that ...
Bml's user avatar
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1 answer
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Mapping between generalized forces and external torque of a rigid body whose rotation is described by quaternion is not unique(?)

In this paper the mapping between generalized forces and external torques for a rigid body (when the rotation is described by a quaternion) is derived: $$\textit{F}_Q = 2\textbf{G}^TT'$$ where $\...
blenderman's user avatar
5 votes
2 answers
1k views

Why can we treat a ball as a point mass to calculate torque?

A sphere of radius $R$ is supported by a rope attached to a wall as shown in the below figure. The rope makes an angle $\theta$ with respect to the wall. The point where the rope is attached to the ...
Ryder Bergerud's user avatar
1 vote
2 answers
146 views

Resolution of Ehrenfest paradox using only special relativity

It was my understanding the solution to the Ehrenfest paradox requires non-Euclidean geometry. Observers riding the rotating disk measure small distances according to the Langevin-Landau-Lifschitz ...
Aiden's user avatar
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7 votes
4 answers
602 views

Does a rocket moving in a circle expel exhaust at a greater velocity?

Consider a rocket undergoing constant acceleration in a rectilinear path. Assuming the rocket is ideal (ignoring fuel mass and energy loss such as sound, radiation, vibration, etc.) a portion of the ...
Trever Thompson's user avatar
2 votes
2 answers
187 views

Is angular velocity about any point in a rigid body always the same?

Suppose I have a disc that is in translational as well as rotational motion. Question 1: If we talk about the angular velocity of the disc, about which point is this angular velocity measured? (I mean ...
User's user avatar
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1 vote
1 answer
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Tendon excursion method application/alternative for joint represented by quaternion in biomechanics

I am building a biomechanical model that consists of spherical joints. I wanted to represent these spherical joints by quaternions. I am struggling to derive how the muscles contribute to the ...
blenderman's user avatar
1 vote
1 answer
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Can the motion of a rigid body be decomposed into translational and rotational motion about ANY point?

My textbook mentions Chasles' theorem which asserts that " it is always possible to represent an arbitrary displacement of a rigid body by a translation of its center of mass plus a rotation ...
Vulgar Mechanick's user avatar
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3 answers
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Why does moment of inertia stop at 1/2 as solidness of a cylinder increases?

So I have two things about moment of inertia: The I for a hoop is $I=MR^2$ and the I for a solid disk is $I=\frac{1}{2}MR^2$ I've noticed that as "solidness" goes up from 0% (completely ...
Shelby Longbottom's user avatar
2 votes
1 answer
54 views

Spinning a rope conundrum

Sometimes I will take a rope or string and spin it in the air to see what will happen. Now usually, if I am spinning it vertically, the end of the rope will extend outwards due to Newton's first law, ...
Frontiers Aerospace's user avatar
2 votes
2 answers
95 views

Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?

The tennis racket theorem (whose effect is also known as Dzhanibekov effect), states that the rotational motion around the intermediate principal axis is not stable (that is, any small disturbance ...
ebenezer's user avatar
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1 vote
2 answers
91 views

Why doesn't centrifugal force change instantly?

If I'm riding my dirt bike on a rocky road, centrifugal force keeps the front wheel rolling in a straight line so I can take my hands off the handlebars without worry. But if I hit a rock and the ...
foolishmuse's user avatar
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0 answers
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Calculating the amount of torque applied to to stop a rod rotating at some angular velocity

Consider a Rod AB, having length $l$ with non uniform mass density $\lambda (x) $ a function of length from the end A, is rotating at an angular velocity $\omega$ with fixed end A and free end B. ...
Gajjze's user avatar
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-1 votes
1 answer
33 views

Implicit definition of internal forces through choice of dynamical description of a rigid two mass pendulum

The central mass theorem states that the center of mass of a N-body system moves as if all external forces acting on the bodies of the system acted directly on the center of mass, it is a generic ...
hijit's user avatar
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0 votes
2 answers
57 views

Rolling ball on a surface with friction

For a point particle moving on a surface under the infuluence of gravity, the equation of motion is very easy to write down - the force on the particle is simply the projection of its weight $mg\...
FusRoDah's user avatar
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1 vote
1 answer
61 views

Coriolis force on a particle moving on sphere

Consider a particle moving on a rotating disc, as shown below. The direction of the Coriolis force acting on the particle can be found using the cross-product of the angular velocity vector and the ...
Utility ZC's user avatar
2 votes
2 answers
59 views

Do off-centre forces create additional energy?

When a force is applied to a rigid body at its centre of mass, it accelerates. Over time, that acceleration becomes velocity, which gives the body a certain amount of kinetic energy. However, if that ...
oak's user avatar
  • 23
2 votes
1 answer
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Motion of bowling ball

I'd like to model the motion of an asymmetric bowling ball thrown on a bowling lane. I know there's forward momentum and angular momentum that moment the ball is released, and there's of course ...
Lex_i's user avatar
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0 votes
1 answer
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Avoiding secondary flow in rotating fluid

I am required to create an annular flume for an experiment. The flume is to be filled with water, and a paddle is to be dipped into the water and rotated along the flume at some fixed angular velocity ...
CasioWave's user avatar
1 vote
0 answers
29 views

Relationship between varying radius of ball and its affect on time taken for ball to come to rest in a spherical hemisphere while moving in a circle

I am a high school student trying to figure out the theoretical relationship between the radius of a ball that is launched into a bowl (moves in a circular path in the bowl) and the time taken for it ...
suryabh asjdncw's user avatar
0 votes
3 answers
64 views

Doubt regarding angular momentum conservation

in the above question I have doubt regarding validity of angular momentum conservation. The question is solved by conserving angular momentum about axis of larger disc as follows; $$0 = -\frac{1}{2} M(...
user1308446's user avatar
1 vote
1 answer
48 views

Why isnt the contact force between the rack and wheel 200N?

I was looking at this YouTube video 'Example 1' (from 4:17 timepoint) and wondering why the contact force F between the rack and wheel isn't also 200N? Isn't this constant force of 200N being ...
Dubious's user avatar
  • 121
0 votes
2 answers
63 views

Rotation of a mass attached to a spring

Consider a case where a ball or object of mass $m$ is attached to a spring that is hinged at one point. If the ball is given a velocity perpendicular to the spring, it does spiral motion due to ...
Okayy 3455's user avatar
1 vote
0 answers
33 views

Does moving the idler in a wheel and disk CVT conserve energy or momentum? [closed]

Consider the wheel and disk CVTs (continuous variable transmissions) below. Configuration A comprises a CVT disk coupled to the "system under control" 's', whereby a control wheel 'cw' ...
Mr. Haelscheir's user avatar
1 vote
1 answer
46 views

Does the direction of the torque acting on a car tire change depending on which direction the tire is rotating?

As I understand, the reason why unbolted car tires will fly off perpendicular to the direction of a moving car is because of the torque generated by the axel. This is unintuitive to me because there ...
thomparte's user avatar
1 vote
1 answer
60 views

Question on rotational dynamics

My book states that it's convienient to apply torque equation $\tau=I \alpha$ on instantaneous axis of rotation and centre of mass. My question is: why it is so? And how can we apply torque equation ...
NAITIK VERMA's user avatar
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1 answer
35 views

Energy loss on increasing moment of inertia

A body connected to a inextensible, massless string which is being spun around by a man in a circular path. The rope is then slowly released by the man from his fingers and stopped at a certain radius....
Kyathallous's user avatar
11 votes
5 answers
4k views

If you're holding on to a playground spinning wheel and then let go, is your trajectory straight or curved?

Let's say you are on one of those playground spinning wheels and then you let go. I've heard that you will fly off tangentially to the wheel, but do you really fly off in a straight line, since you ...
scm's user avatar
  • 776
0 votes
2 answers
44 views

Why am I getting this derivation of time period of pendulum in an accelerated frame wrong? [closed]

We are working in the frame of the cart and we are trying to obtain the $\tau=k\theta$ form. So, let's write the $\tau=I_{axis}\alpha$ first for a small deviation $\theta$ from the vartical. (The ...
Swan's user avatar
  • 80
1 vote
0 answers
24 views

Evolution of a rotating system in which mass continually leaks [closed]

this might be a trivial problem but me and a friend have failed to solve it. This is not homework, it actually relates to a book of mine but that is of no interest. Imagine the following; Two masses $...
ErikHall's user avatar
  • 308
1 vote
1 answer
74 views

Is the idea of a rigid body compatible with Newtonian mechanics?

It is known that rigid bodies cannot exist in the framework of special relativity by causality arguments. But recently I saw a video on YouTube that claims rigid bodies are not compatible with ...
Jonathan Huang's user avatar
0 votes
1 answer
33 views

Spinning top stabilisation for a type of aircraft/drone

Spinning tops use gyroscopic precession to be able to stay upright whilst spinning. Would it be possible to use this phenomena to create a flying craft that would be stabilised by gravity and the ...
Angus's user avatar
  • 1
0 votes
2 answers
54 views

How does the centripetal force on the butt of a golf club's shaft produce torque that rotates the club/clubhead forward?

In the top picture, which is how torque is typically explained, the center of rotation is different than in the bottom picture. I think I understand how this works in the top picture, but I don't see ...
delusionist's user avatar
2 votes
3 answers
235 views

How can we choose two different mass moment of inertias for the same momentum calculation?

I am working on answering part (a) and here is what I got: By conserving linear momentum, we have that $$mv_0 =(3M)v_f \hspace{3mm}\implies \hspace{3mm} v_f =\frac{1}{3}v_0$$ Now, in order to conserve ...
Chris Christopherson's user avatar
0 votes
1 answer
33 views

Spinning plate on the barbell

Suppose I have a plate and a barbell like the ones we see in the gym. When I spin the plat in the clockwise direction, the barbell also starts spinning in the clockwise direction. When I put my hand ...
sshi's user avatar
  • 1
0 votes
1 answer
58 views

How torque and linear force interact with forces on poles

When there are 2 forces normal to each end of a uniform pole, if they had the same force, the rotation would be cancelled out and all force would be acting in one direction. But if one force was ...
Charlie Parker's user avatar
0 votes
1 answer
63 views

Does spinning the umbrella slow down the fall more?

Ignoring its structural weakness, if you jump from some height and use an umbrella to slow down the fall, would making it spin while you're falling affect the speed in any way?
Flamethrower's user avatar
0 votes
1 answer
145 views

Spring hanging on a spinning Disk

I have already asked a question on the Math stack-exchange. You can find it under the following link: https://math.stackexchange.com/q/4876146/ I felt like the question is better suited for this stack-...
Mo711's user avatar
  • 89
1 vote
0 answers
62 views

Angular momentum ABOUT centre of mass (Investigating this IITJEE 2016 problem.....) [closed]

Note- By COM i mean the Centre of mass. In this question , I analyzed a problem in mechanics and encountered a difficult situation which the problem doesn't address (and so do my teachers ) ...... ...
Ninjametry's user avatar
1 vote
1 answer
41 views

Proof for conservation of angular momentum in rotating frame of reference

imagine a simple situation such that an object is rotating on a table about a rope as seen in the below figure now if i pull on the rope from the center , the radius of circular motion of the object ...
Arnav Agarwal's user avatar
0 votes
3 answers
152 views

What happens if we prevent gyroscope to precess?

If we apply some torque to spinning wheel in a vacuumed space in body frame y axis, wheel try to precess due to gyroscopic effect but it will be prevented by obstacles as seen from picture, what will ...
pysicsuser's user avatar
0 votes
2 answers
59 views

Why is the centrifugal force multiplied by $\sin$ here?

I'm currently studying for an exam and wondering what the visual interpretation of this question would be. It's a multiple part question and the first question was describing the equilibrium angle of ...
Thabuu X's user avatar
0 votes
1 answer
32 views

A block on a smooth rotating table [closed]

Assume a block is placed on a slightly rough table. Now that table starts to rotate about its center. Why does the block move towards the edge and fall off? I heard somewhere that it is because of &...
Akhilesh G's user avatar
0 votes
0 answers
56 views

How can we show that $((\vec v · \vec r) \vec r )'$ corresponds to Coriolis force?

We have: Position as $\vec r$ Velocity as $\vec v=(\vec r)'$ Acceleration as $\vec a=(\vec v)'$ Angular velocity as $\vec \omega = \frac{\vec r × \vec v}{r^2}$ Angular acceleration as $\vec \alpha = ...
Navneet's user avatar
  • 261
1 vote
1 answer
63 views

Where did the rotational energy come from? [duplicate]

Consider a floating static pencil in flat space with no gravity. If we apply an impact force F for a short time t to the pencil vertically, pencil must get a CM momentum Ft, and corresponding kinetic ...
S tomio's user avatar
  • 31
1 vote
4 answers
50 views

What is angular momentum and torque due to the center of mass? Give me an example

when I was studying angular momentum and fixed axis rotation in kleppner book, I had a topic on motion involving translation and rotation. On that topic, they said that components of angular momentum ...
professor T's user avatar
1 vote
1 answer
62 views

Newton's second law when the force does not pass through the center of mass [duplicate]

If I have a stick with even mass distribution, and for scenario (1) I give it an instantaneous force at the tip, how can I determine the speed of the center of mass? Is it by Newton's second law? ...
paganiac's user avatar

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