In the below picture:Imagine the earth is rotating at angular velocity $( \mathbf{\omega}\space \hat{k})$ rad/s in anti-clockwise direction. The centre of the earth is located at O.A comet B is ...

Around a low-pressure zone in the northern hemisphere, wind blows counterclockwise. Also, cyclones get created when there is a low pressure, and when air is rising. So, naturally, cyclones should spin ...

It's important to remember that water is a good conductor of heat. If a thermometer is fixed statically against a flowing stream, then the impact of water molecules does generate heat that could be ...

In statistical physics we consider the system in its center-of-mass reference frame, so that the velocities of the molecules that are relevant for temperature are those in this reference frame, and ...

This might be handled as game theory. The mosquito is a point particle with limits on how fast it can fly and accelerate. It is trying to avoid some sort of fly swatter with limits on how fast it can ...

You're right to question the use of Bernoulli in compressible flow situations. When $v_1$ is large and the area ratio $A_1 / A_2$ is significantly greater than 1, the incompressible Bernoulli equation:...

When water flows down a constant slope, it keeps a constant average speed. Potential energy turns to kinetic energy and then to heat. This does heat the water.A typical speed for flowing water is ...

You can do it either way.The temperature is not frame-independent.If you define a frame where a particular fluid portion is at rest, your temperature calculation will exclude the bulk motion and you ...

I read three abstracts of the autor you linked, they were on history of physics so I don't exactly understad why you linked him this way.Also, the Coriolis forse arises in any non-inertial rotating ...

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The problem is that you are thinking that the two spools are essentially independent of each other. The string enforces a constraint between the two of them and you actually need to handle this ...

To apply a single force F1 at distance d from G is equivalent to applying a torque by -F1/2 at distance -d and F1/2 at distance d. This will make the solid rotate.The motion of G depends only on the ...

A satellite will tend to become tidally locked, so that the same side always faces the primary. If the object has a long axis, tidal forces will tend to align the long axis on the line between the ...

Paradoxes such as this have a long history and their resolution was found long ago and is now also in textbooks (those at a level one above introductory). The concept to keep in mind is that a flow of ...

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The time it takes a vehicle to go from speed $v$ to speed $v + \Delta v$ is given by the integral$$ \Delta t = \int_v^{v + \Delta v} \frac{1}{a}\,{\rm d}v \tag{1}$$where $a = a(v)$ is the ...

As @Mariano G has pointed out, always start with free body diagrams (FBD). Avoid "guessing" or attempting to use "intuition".In this case, draw a FBD for each block individiually. ...

I suggest you start by reviewing how to draw free-body diagrams. It's the first step in virtually every problem of this type. Do not be tempted, as some do, to put the acceleration on the diagram as ...

Spoiler: I won't answer the question about which is the best rpm range to get maximum acceleration, but I'll provide (hopefully) an answer with all the tools you need to find that on your own....

It can also be looked that way. Power can be defined as the rate of change of total mechanical energy. Omitting potential energy, this leads to $$\tag 1 P = \frac {dK}{dt},$$or$$ \tag 2 P = \frac {m ...

A car's wheels are in pure roll. That implies linear acceleration $a$ is proportional to angular acceleration $\alpha.$At max power, $P=Fv=\tau\omega$ has a large $\omega$ and so $\tau$ is small. But ...

The assumption which is made is that the impulse $J$ on the ball due to the stick is much larger than the impulse on the ball due to the frictional force.This idea is illustrated in the answer to the ...

Let's try the reverse engineering. The answer implies $mv_0 h = I_{cm}\,\omega_0$, or$$v_0 = \frac{2}{3}\,\omega_0 R.$$Then$$(F - f)\, t = \frac{2}{3}\, m \omega_0 R,$$and$$\left( \frac{3}{5}...

When an American football is sent rolling down an incline, for example, it typically starts out spinning around its long axis but soon shifts to a rolling motion upright around its short axis. This ...

Think of it this way. It's clear that any number of forces can be summed to one net force. Without losing generality, let's assume a coordinate system where that net force acts in the Z direction. ...

Suppose that the spring is hung from a hook.System = springAt the bottom of the spring an external downward force $F$ is applied on the spring and the spring exerts an upward force $F$ on whatever ...

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Well yeah, the extension is the same. In one case it is you who is pulling the spring from both sides, and on the other case its the wall which pulls from one side and you from the other ( it is the ...

In classical mechanics, the action for a particle of mass $m$ moving in a potential $V(\mathbf{x})$ is$$S_{\text{classical}} = \int \left(\frac{1}{2} m \mathbf{v}^2 - V(\mathbf{x}) \right) dt.$$...

The easiest way to look at this situation is to examine the effect of torque on the ball. There are two forces acting on the ball: a component of the gravitational force $F_g$ acting on the COM of the ...

I don't think you're wrong at all. Consider suction cups or hooks for example. In that case the normal force is indeed as you say, and greater due to the partial vacuum. But it's nigh impossible for ...

The ball initially spinning around x-axis with some angular speed. Some imperfection in the way causes the ball to tilt slightly to one side, for example to the left as shown. As it tilts, its rolling ...

It is not correct that the relevant invariant distance between two points in Newtonian spacetime is $c^2 dt^2 + d\vec{x}^2$.It is true that this quantity is indeed invariant in Newtonian physics (if ...

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A geometrical cube has six faces. If you assume that the faces have a certain mass $m$, the center of mass would be the center of the cube. If you remove the (mass of the ) top face of the cube, this ...

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For a loop, yes. I first saw this problem in Why Cats Land on their Feet by Mark Levi in the chapter "Slithering Ropes in Weightlessness." There is even the sketch of a proof and I will ...

a way that I could show mathematically that the work done by kinetic friction is path-dependent?It is not possible to define a potential energy for the kinetic friction force, even in the simplest ...

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Try using the closed line integral definition of conservative forces: $$\oint_C \vec{F}\cdot d\vec{\ell} = 0$$ for an object moving on a 2D plane with kinetic friction.

Your question is founded on a misconception because the physical significance of a metric is that is is an invariant. The proper distance between two events defined by the Minkowski metric:$$ ds^2=-...

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To recover the classical limit, your just need to reintroduce the speed of light $c$ and send it to infinity:$$ds^2 = c^2dt^2-dx^2$$As you can see, in the non relativistic limit, you do not ...

In the context that you have described the pulley is “carrying” a massless inextensible string which changes a force exerted on the string at one end to an equal magnitude force exerted by the string ...

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Yes, it is true. Since there is no friction there will not be any energy lost to as heat, regardless of whether it spins or not. Since it is massless there will not be any energy stored in the KE, ...

A an elastic chain of mass points in 3D coupled elastically to both next neighbors with free ends reduces to a center of gravity point with total mass, moving with constant velocity. Stay in its rest ...

Consider the energy perspective. Tension cannot do work on the object. If uniform circular motion, KE of object cannot change. If friction present, the object will slow down, which is a contradiction.

Since your feet don't move due to friction, your body is acting like a lever with a pivot point at your feet so in addition to the linear deceleration force there is also a moment force that is a ...

The actual point of rotation does not matter; either approach is OK if you do the bookkeeping correctly. Consider a pendulum NOT attached to the moving cart but instead just pivoted at one end (or, ...

No. Gears don't increase energy, they increase torque. The energy you can get out of this contraption is just the energy you put in when you lift the weight up. This doesn't change, no matter how many ...

f is a tricky term because it looks like the Earth rotation whereas it is the opposite of the rotation R' caused by the Coriolis force.The Earth rotation causes a forcing R' with a sign opposite to f!...

To do this, you need to know the heat transfer coefficient to the external medium, as determined by separate considerations (such as experiments or correlations).

To answer your question 1: Because some energy is related to a fixed length, while some energy is related to a variable length.To answer your question 2:This is because energy is not a real thing.

you seem to place too much importance on kinetic energy. There is only one deformation, which is determined by the relative speed of approach of the two given objects, not by kinetic energy. In your ...

The rod is accelerating so each part of the rod must have a net force on it.Consider a line of fours masses, $m$, connected together as shown below in the free body diagram and the right hand mass ...

The short and unhelpful answer is that the rolling motion at start is unstable, and the end-over-end rolling is stable. Why is this?At the beginning, if the football gets a slight kick--from ground ...

An elastic rod moving horizontally with acceleration $a$ is deformed in the same way as a rod in equilibrium, hanging in a gravitational field with $g = a$. The difference in tension between any two ...