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10 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 ...
jwimberley's user avatar
  • 3,878
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 ...
KDP's user avatar
  • 5,851
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 ...
mmesser314's user avatar
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5 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 ...
RC_23's user avatar
  • 9,463
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's user avatar
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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 ...
Roger V.'s user avatar
  • 60.1k
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 ...
Bob D's user avatar
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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 ...
mike1994's user avatar
  • 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, ...
Cleonis's user avatar
  • 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 ...
Cleonis's user avatar
  • 21.4k
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=\...
Pato Galmarini's user avatar
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)...
ABetheGammow's user avatar
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 ...
Farcher's user avatar
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1 vote

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 (...
WillO's user avatar
  • 15.9k
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 ...
Claudio Saspinski's user avatar
1 vote

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

car tires will fly off perpendicular to the direction of a moving car I'm not sure this is true. I've seen cases where they move in about the same direction the car was. because of the torque ...
joseph h's user avatar
  • 29.9k
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, ...
Claudio Saspinski's user avatar
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 ...
basics's user avatar
  • 10.6k
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 ...
mike stone's user avatar
  • 54.5k

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