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In simplest terms and using Newton's mathematics: F = m * a. or Force F = mass m * acceleration a. Example #1 - A body on Earth. Now on the planet Earth, the gravitational acceleration "g" is about equal to 9.8 meters/second^2. So let's substitute a=g in the above equation. Then the force required to keep an object of mass m AT REST near the surface of ...

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We introduce the $Q$ factor in order to describe how much of the oscillator's energy is lost due to friction in one cycle of oscillations. For it to be of any practical use, the $Q$ factor must be a constant (i.e. time-independent) function of the oscillator's parameters. It should be equally applicable to damped oscillations, as well as steady-state driven ...

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First of all you cannot separate linear from angular momentum. They work together just like linear and angular velocities do (or forces and torques). I am going to answer your question from the perspective of geometry. The quantity of momentum is not so important as the geometrical construction that momentum implies. Let's see if you can follow: All ...

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I suppose Newton may have devised the momentum equation to numerically express how objects of exact speeds (but different densities) would create different effects upon impact and perhaps how much energy would be needed to move such objects to a given speed. Consider the following: a wood ball (25g, 33.5 cc) hurled at a sheet metal target at an average ...

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What you're looking for is an intuitive explanation or how you could visualize momentum. You can think of momentum as the quantity/amount of motion or "how much would I not want be in the path of this body." I'm going to try and provide some intuition through a few examples: A car of mass 1000 kg moving at 5 m/s would have the same "quantity/amount of ...

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Newton (if I recall correctly) typically referred to the concept of inertia, which was an objects resistance to changes in velocity when subjected to external forces. You are right about him not thinking about it as just the speed of the object, because this is where the mass term comes in. Many people think of Newton's second law as being written as $F = ... 3 Newton thought of momentum as "Quantity of motion" - as we can see in the translated version of 'Principia'. Particularly, he defined momentum in the following words: The quantity of motion is the measure of the same, arise from the velocity and quantity of matter conjointly. So yeah, that is the definition of momentum. The question why we defined the ... 2 One thing that may help you is to understand that work is an expenditure of energy. For instance, if you push a rock up a hill, you exerted a force over a distance, so you had to use energy. But the coat hanger in your closet isn't expending energy, even though it's exerting a force to hold itself up over a period of time - because it isn't moving over any ... 0 First of all, forces accelerate an object when the net force is not zero. If friction is present, it actually does accelerate an object. Acceleration is defined as the change of velocity over time. This is not limited to increasing speed. Gravity also can accelerate an object. Work is just defined as$Fd\$ (force times distance) just because it is useful. ...

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Its only the more elementary math textbooks that use the opposite convention. Every physics book puts the conjugate first. And when you get to more advanced operator theory math books eventually everyone switches to the other convention because it does make things easier. And the only reason math books do it the wrong way is so they can use the word ...

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To be honest it doesn't matter unless and until one of them is complex conjugated and the same is maintained throughout the course. Most books I have come across conjugate the first term.

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As a rule of thumb, in mathematics a complex inner product or sesquilinear form is conjugate-linear/antilinear in the second entry (in the tradition of listing the least complicated arguments first), while in physics it is the other way around: It is conjugate-linear in the first entry (in order to make contact to the Dirac bra-ket notation).

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