90
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 ...
- 88.9k
75
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 ...
- 42.6k
41
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^...
- 50.4k
38
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 ...
- 2,070
32
votes
Spinning gyroscope loses weight?
You are substantially overstating the precision of your measurements.
The readings changed rapidly so they had to be read by stepping through videos of the experiment.
What you mean is that you ...
- 105k
30
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, ...
- 934
25
votes
Accepted
Does rigid body rotation contradict Newton's first law?
First of all, a more precise statement is that "an object will move with constant velocity if there is no external force acting upon it". This is the same as saying the object moves in a ...
- 13.9k
23
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 ...
- 15k
23
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 ...
- 1,201
23
votes
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 ...
- 3,052
23
votes
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 ...
- 98.6k
22
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 ...
- 4,565
20
votes
Accepted
Why a moving car dips to front when brakes are applied?
Take the centre of mass as the pivot point. Weight passes through the centre of gravity, which is practically the same position as the centre of mass, and so contribute nothing to the angular ...
- 9,908
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 ...
- 30k
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 ...
- 58.1k
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♦
- 16.5k
17
votes
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 ...
- 7,211
17
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 ...
- 75.6k
15
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 ...
- 46.8k
14
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 ...
- 38.9k
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 ...
- 98.6k
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 ...
- 359k
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) ...
- 57.5k
13
votes
Spinning gyroscope loses weight?
One thought as to why you might see this: Is your gyroscope perfectly balanced?
If not, it will generate up and down forces as it spins. At one instant, it will press down harder on the scale and be ...
- 42.6k
13
votes
Spinning gyroscope loses weight?
A lot of people have been misled by this apparent effect, notably Eric Laithwaite in his later years1.
I suggest that you need to be able to collect six-axis data at the point of contact, ...
12
votes
Is it correct to say that it is theoretically impossible for perfect rigid bodies to exist?
Not quite. You are correct that rigid bodies do not exist, but this is not the reason. Your assumptions imply that for a velocity to go from a positive value to a negative value, it must go through ...
- 50.6k
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 ...
- 6,253
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.
- 55.2k
11
votes
Accepted
Why does a smooth rolling ball roll indefinitely despite there being static friction?
Real rolling objects on a horizontal plane (i.e., for $θ=0$) do not slow down due to static or dynamic friction but aerodynamic drag and rolling friction (caused by deformation of the rolling object). ...
- 6,359
Only top scored, non community-wiki answers of a minimum length are eligible