11
votes
Accepted
Why can we treat a ball as a point mass to calculate torque?
Calculating the torque on a rigid body w.r.t to the point $\vec 0$ (WLOG) with gravity pointing in a constant direction $\hat n$ is accomplished by integrating over the rigid body, with each ...
- 3,888
8
votes
Does a rocket moving in a circle expel exhaust at a greater velocity?
This is an interesting question, because when it is moving in a circle, the magnitude of its tangential velocity is constant and its angular velocity is also constant. Therefore the total kinetic ...
- 6,102
6
votes
Accepted
Why doesn't centrifugal force change instantly?
This behavior is not caused by centrifugal force, but rather by conservation of angular momentum.
If you take any spinning object, and draw an arrow aligned with the axis of rotation, that arrow ...
- 9,500
5
votes
Does a rocket moving in a circle expel exhaust at a greater velocity?
The energy of the fuel does become the kinetic energy of the exhaust.
Let us ignore the fact that the rocket becomes lighter as it burns fuel, and that it will eventually run out of fuel. The rocket ...
- 41.1k
4
votes
Why does moment of inertia stop at 1/2 as solidness of a cylinder increases?
The reason that the moment of inertia gets smaller as the annulus gets less like a hoop and more like a disc is that more of the mass is closer to the axis of rotation. You can make the moment of ...
rob♦
- 91.5k
3
votes
Why can we treat a ball as a point mass to calculate torque?
The torques can be calculated in respect to any point, and it generally requires taking integrals. However, there are some basic tricks to simplify life. One of them is choosing the rotation axis at ...
- 60.3k
3
votes
Is angular velocity about any point in a rigid body always the same?
Doubt 1
It is measured about the axis of rotation.
Doubt 2
Yes.
For a rigid body all points will complete one revolution, $2\pi$ radians, about any axis of rotation in exactly the same amount of ...
- 73.7k
2
votes
Implicit definition of internal forces through choice of dynamical description of a rigid two mass pendulum
You are using two different theorems as if they were equivalent, but they are not. Both theorems come from studying a system of particles. The theorem you use in rotational dynamics is that $\tau=\...
- 795
2
votes
Accepted
Spinning a rope conundrum
You are exciting standing "circularly polarized" waves in the rope. If you continue to spin at a faster frequency, you can create even more "nodes" in the rope (stable points of ...
- 978
2
votes
Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?
I'm posting a new answer for the following reason: a totally different way of implementing a Dzhanibekov effect demonstration occurred to me.
Manufacture an object that is spherical on the outside, ...
- 21.4k
2
votes
Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?
A gimbal suspension for the purpose of demonstrating the Dzhanibekov effect (when weightlessness is not available) presents special challenges.
In a comment I already linked to the video about the ...
- 21.4k
2
votes
Is angular velocity about any point in a rigid body always the same?
Each part of the rotating disk will have the same angular velocity. However, they will not all have the same tangential velocity (which will increase as you move further away from the axis of rotation)...
- 96
2
votes
Accepted
Do off-centre forces create additional energy?
If the line of action of the force is not through the centre of mass then body can be thought of as being acted on by a force whose line of action is through the centre of mass which produces a linear ...
- 97.9k
2
votes
Accepted
Resolution of Ehrenfest paradox using only special relativity
Instead of a solid disk, we might as well think of a circular train traveling on a circular track.
Alice sits in the station. Bob is riding on the train.
The Question: The track is shorter in Bob's (...
- 15.9k
1
vote
Why is the moment of inertia the rotational analog for mass and not inertia?
There are two aspects of mass. One is inertia, defined by Newton's second law, F=ma. The other is gravitational mass, defined by Newton's law of gravity, F=Gm1m2/r2. They are the same in relativity, ...
1
vote
Why is the moment of inertia the rotational analog for mass and not inertia?
but in my textbook the definitions of inertia and moment of inertia
are very close to one another
They are. The term "moment" is synonymous with the term "torque" which is is ...
- 73.7k
1
vote
Conservation of linear vs. angular momentum in two similar cases
It is a valid question, that in case 1 it seems that momentum shouldn't be conserved due to the horizontal force of the pivot point. The simple answer to this question is that, the pivot point does ...
- 278
1
vote
Does a rocket moving in a circle expel exhaust at a greater velocity?
Energy is frame dependent.
In a inertial frame that is momentarily comoving with the rocket, its kinetic energy is zero, and the kinetic energy of the gas is the same for both cases, if we suppose the ...
- 16.7k
1
vote
Why does moment of inertia stop at 1/2 as solidness of a cylinder increases?
The moment of inertia comes from the definition of angular momentum for a particle $\vec L = \vec r \times \vec p$. In the case of a disk, $\vec r$ is always perpendicular to $\vec p$ for any point, ...
- 16.7k
1
vote
Why doesn't centrifugal force change instantly?
Looking from above, when any spinning wheel is nudged anticlockwise it always responds by trying to rotate the spin axis so that the axis is vertical and the wheel is rotating anticlockwise around the ...
- 6,102
1
vote
Accepted
Coriolis force on a particle moving on sphere
Considering only Earth rotation around its axis with angular velocity $\boldsymbol{\Omega}_E = \Omega_E \mathbf{\hat{z}}$, you're right that at the equator there is no Coriolis force on a point that ...
- 10.7k
1
vote
Do off-centre forces create additional energy?
There is a standard demonstration in which an off-centre force is provided by a string wrapped around a cylinder on a air-table. Another string is connected to the c-of-mass of an otherwise ...
- 54.5k
Only top scored, non community-wiki answers of a minimum length are eligible