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3

In a rotating reference frame, the coordinate velocity of an object can exceed $c$. However, this doesn't mean that they're moving "faster than light". If we were to look at the light-cones at these distant locations, we would see that the four-velocities of these objects are still confined within the light-cones at those locations. To put this another ...


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Let's consider two ships passing each other. When they pass, a rope is thrown from a ship to the other ship. Then then rope is pulled sharply. That causes the ships to collide, the rears of the ships hit each other and the ships start to spin. In the previous scenario part of the energy used to pull the rope became rotational energy of the ships, that ...


3

How does the kinetic energy of a ballerina increase? Conservation of angular momentum: $$L_1=L_2 \implies I_1\omega_1=I_2\omega_2\quad\quad (1)$$ Pulling in your arms reduces moment of inertia $I$, since the same mass is now distributed over a volume closer to the spin centre, $I=\sum mr^2$. As you say, reducing $I$, so $I_2<I_1$, implies ...


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But when I look at it from an inertial frame, I cannot intuitively understand how does the spinning of the Earth makes the mass free falling more slowly than when the Earth is not rotating? In the inertial frame, the mass will have the same radial acceleration whether rotating or not. But on a rotating earth, the mass also has a tangential speed. ...


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(I've read your question yesterday and could not find peace because of it, since I could not answer it to myself satisfactorily. ^^ But I figured it out and I hope the following helps... ) They key point is that, if the gravitational force acts as a centripetal force, the amount of centripetal force needed to let an object go round a circle with angular ...


1

All the stars would be attracting each other and hence the would stick to each to attain equilibrium. Why doesn't this happen? You are forgetting angular momentum. Consider a binary star pair. Ignoring the expansion of spacetime, and in the absence of some mechanism that removes angular momentum from the system, those stars will orbit one another ...


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I think the answer must be either the book has got it wrong or that there is some confusion between what the author meant to put in the book and the question before us. If I understand the question correct the point is does an object falling towards a planet undergravity have different acceleration (different dynamics) depending on whether the earth is ...


1

All the stars would be attracting each other and hence they would stick to each to attain equilibrium. Why doesn't this happen? This is an old question. Even Newton himself had thought about this question. His idea was that in long distances or separations (say, inter-galactic distances) the force of gravity might appear to be repulsive. That's why not ...


-1

If there would be initial rotation(as we see most of all objects today are rotating around another) gravitational force is accounting for the centripetal force. I'm new here so, I don't know how to type the equations, but I hope you get my point. Further many objects are there which have many other forces, like Coulombic force(when charged bodies are ...


1

I'm not fond of calling centrifugal force an "imaginary" force. I prefer to explain it in terms of reference frames: In an inertial reference frame, Netwon's laws are sufficient to model (non-relativistic) motion. In a non-inertial reference frame, additional forces (like centrifugal, Coriolis, etc.) must be added to the model. What makes centrifugal ...


2

For a 3-minute video I think I would avoid both concepts. Centrifugal force can be a confusing concept for several reasons (not least of which that the mere mention of the term tends to attract pedantic know-it-alls who have decided it's their task in life to derail every discussion with loud patronizing explanations of how it doesn't exist at all). Since ...


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It is wrong to say they are the same. I suspect for a short video that it would be better to choose one which is most relevant for your purpose and not mention the other. Centripetal force is any force pulling inwards on an object to maintain its motion in a circle - in your case the force of your arm pulling on the bucket as it swings. Centrifugal force ...


1

Centripetal and centrifugal forces are only equal for an object being held stably in a rotating system. A good analogy is the difference between 1) the force of gravity and 2) the supporting force of the ground pushing up on you. Centrifugal forces and gravity aren't quite proper forces since they are really more like fixed accelerations; to represent them ...


0

Here's how you might explain the difference between the two forces to your class: When you're whirling a bucket of water, centripetal force is carried by your arm, the rope, and the bucket. It points inward toward your shoulder, which is the center of the circle formed by the whirling bucket. Centrifugal force is caused by the inertia of the water in the ...


7

There is definitely a huge difference. Centripetal force is a real force that causes objects to move in a circular path or curved path that points to the center of the circle or curvature respectively. Centrifugal force is not a real force. It is an inertial force established so that Newtonian laws are valid when observing motion in an accelerated frame of ...


4

Centripetal force is the force that an object feels when is in a circular motion. In this picture, ac is the centripetal force, v tangencial velocity and w angular velocity. Now, centrifugal force is the imaginary force that appears when the reference frame is on rotation.



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