91
votes
Accepted
Why don't helicopters use reaction wheels to counter the main rotor?
You're talking about a device (in helicopters the tail fan imparting horizontal thrust) that counteracts the torque imparted on the main rotor (and therefore on the helicopter) by the surrounding air ...
- 86.7k
70
votes
Accepted
Is it correct to say that it is theoretically impossible for perfect rigid bodies to exist?
You are right. Perfectly rigid bodies are an idealization, like point particles or massless frictionless pulleys. They do not exist.
But they are useful. Plenty of objects exist that are so rigid that ...
- 31k
62
votes
How can the contact point of a body rolling without slipping have zero velocity?
What luck! Just yesterday I was thinking about this exact same phenomenon whilst watching the film 'The Imitation Game'; the title sequence contained a moving tank.
When I was little, I used to ...
- 998
39
votes
Accepted
Why certain rotations are unstable? (Euler Equations)
There is another nice way of seeing this mathematically. It is not too hard to show that in the body frame, there are two conserved quantities: the square of the angular momentum vector
$$
L^2 = L_1^...
- 43.7k
37
votes
How is length contraction on rigid bodies possible in special relativity since definition of rigid body states they are not deformable?
Buzz's answer is correct in that there's no such thing as a perfectly rigid body in relativity. But even more importantly for your question, a body in uniform motion does not feel any kind of ...
- 2,050
31
votes
Accepted
Does a rotating rod have both translational and rotational kinetic energy?
It depends what you consider to be the "pivot" about which the rotational kinetic energy is calculated here:
If you choose the pivot as the end of the rod that is physically held in place, ...
- 904
23
votes
Does a rotating rod have both translational and rotational kinetic energy?
You have to understand that concepts like rotational kinetic energy are just shortcuts to solve problems efficiently.
In Classical Mechanics, we start by defining concepts like kinetic energy on point ...
- 4,129
23
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When we say a rigid body is a system of particles, what exactly are 'particles' here?
TL;DR Never forget that we are talking about models here. We know that they cover only part of reality, but they are good enough and much easier to handle than "the full story".
A model need ...
- 2,476
23
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How does the parallel axis theorem explain the opening of a door?
How does the parallel axis theorem explain the opening of a door? - It doesn't.
The moment of inertia of a door does not depend on where you push it.
The torque that you apply to a door depends on the ...
- 84.9k
22
votes
Accepted
Will a pure rolling cylinder stop on a rough surface?
As Yashas Samaga said, it will not stop on a smooth, but frictional surface. It will stop however on an actual rough surface (as it does in reality – e.g. a steel marble rolling on a rough stone ...
- 14.2k
22
votes
Accepted
How can friction do no work in case of pure rolling?
In a scenario of pure rolling of a rigid wheel on a flat plane, you don't need any friction. Once the wheel is rolling, it will continue to do so, even if the friction coefficient becomes zero. If ...
- 1,181
21
votes
Accepted
Why does a Yo-Yo sleep, and then awaken?
If the yoyo is spinning without winding the string, then it must be that the friction between the inner barrel and the string is insufficient to lead to winding.
A flick of the wrist or some other ...
- 848
19
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What do people actually mean by "rolling without slipping"?
The above answers are all good but i want to give another example which really helped me with understanding what does it mean that the point of contact has a velocity of zero.
Think of the 'spinning ...
- 293
19
votes
Motivation for the definition of angular momentum?
Angular momentum is a conserved quantity$^1$. This is an experimentally confirmed reality, and the equations you talk about naturally follow from this fact since one of them defines this conserved ...
- 27.2k
18
votes
Accepted
How can different points on a rigid body move with different speeds but also be relatively at rest?
Having a non-zero relative velocity is fine as long as the distance between the points isn't changing. This certainly holds for a rotating rigid body. As another example, take a ball on a string and ...
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18
votes
Does a rotating rod have both translational and rotational kinetic energy?
Since the rod's center of mass is changing, does this mean that it
also has translational kinetic energy?
Yes.
You have both translational kinetic energy and rotational kinetic energy.
The ...
- 62.9k
18
votes
Accepted
How is length contraction on rigid bodies possible in special relativity since definition of rigid body states they are not deformable?
Perfectly rigid bodies are not possible in relativity, although this is not directly related the Lorentz contraction mentioned in the question. One immediate consequences of relativity is that no ...
Buzz♦
- 14k
17
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Will a pure rolling cylinder stop on a rough surface?
Assumptions made in this answer:
By rough surface, you meant a flat surface which has friction.
The cylinder/sphere/disc/etc. are ideal; they do not deform.
This is my reasonable guess; I am aware ...
- 7,033
14
votes
Accepted
How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?
Keep in mind that the screw axis does not have to pass through the body. For your example place the axis of rotation parallel to the x axis straight above the cylinder, then rotate the cylinder 180° ...
- 5,153
14
votes
Why certain rotations are unstable? (Euler Equations)
There's an alternative to @MichaelSeifert method which uses angular momentum and moments of inertia: it is to deal with the vector $\vec\omega$ directly as we are interested in the evolution of this ...
- 42.2k
13
votes
How can friction do no work in case of pure rolling?
The pure rolling here is under a constant external force on the object so friction does act.
As an example consider an object rolling, without slipping, down an inclined plane.
There will be a ...
- 84.9k
13
votes
Accepted
Rigid body rotation apparent energy paradox
The problem here is that no force can be perfectly impulsive because then the distance moved while the force was being applied would be zero and therefore the work done would be zero. If we assume ...
- 343k
13
votes
Objects falling from table
If the centre of gravity of the object is vertically above the edge of the table then the object is in equilibrium. However, this equilibrium position is unstable (like a pencil balanced on its point) ...
- 40.8k
12
votes
How can the contact point of a body rolling without slipping have zero velocity?
Consider a point $P$ on the surface of the wheel. If you look at the horizontal velocity of that point in the frame of reference of the wheel (axis stationary), then for a wheel of radius $r$ with ...
- 118k
12
votes
Accepted
When we say a rigid body is a system of particles, what exactly are 'particles' here?
In macroscopic mechanics (in other words, "usual" mechanics), a "particule" is a mesoscopic system.
The mesoscopic scale is an intermediary scale between microscopic and ...
- 5,289
12
votes
Why do we talk about inertia tensor?
A rank 2 tensor is something that relates two vectors. In this case, the MMOI tensor relates the rotational velocity vector to the angular momentum vector.
Given a solid whose internal particles are ...
- 35.7k
11
votes
Why does a Yo-Yo sleep, and then awaken?
Its really a great question and let us go by simple definition.
Defination:
As per what wikepedia says:
A yo-yo (also spelled yoyo) is a toy which in its simplest form is an
object consisting of an ...
- 1,830
11
votes
How can different points on a rigid body move with different speeds but also be relatively at rest?
If the velocity of point B relative to point A is always at right angles to the line AB joining them, then the distance does not change.
- 46.6k
Only top scored, non community-wiki answers of a minimum length are eligible