Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.
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Can a fly pierce itself onto a cactus needle?
Somebody on reddit posted a ridiculous picture today of a fly pierced onto a needle of a cactus: http://www.reddit.com/r/pics/comments/xarue/what_are_the_odds_of_this_accident/
Whilst the OP claims ...
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1answer
1k views
What's the right way to calculate the principal moment of inertia?
I am writing a program that incorporates calculating the principal moment of inertia for a protein residue based on its component atom XYZ coordinates. I am exceedingly confused about which formulas ...
2
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1answer
123 views
Symplectic integrators of the pendulum equation?
In particular, a symplectic integrator to solve:
$$\ddot{\theta} + \dfrac{g}{l} \sin(\theta) = 0.$$
I'm currently using velocity verlet - by realizing that
$$\ddot{\theta} = -\nabla (-cos(\theta)) ...
2
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1answer
151 views
How can Hilbert spaces be used to study the harmonics of vibrating strings?
The overtones of a vibrating string.
These are eigenfunctions of an associated Sturm–Liouville problem.
The eigenvalues 1,1/2,1/3,… form the (musical) harmonic series.
How can Hilbert spaces be ...
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1answer
490 views
The trajectory of a projectile launched from a hilltop
Here is the problem:
A boy stands at the peak of a hill which slopes downward uniformly at angle $\phi$. At what angle $\theta$ from the horizontal should he throw a rock so that it has the greatest ...
3
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1answer
491 views
Combining Proportions to get Newton's Law of Universal Gravitation
I've read a little on the history of Newton's Law of Gravitation and noticed that the formula can be separated into 3 distinct parts that lead to the end result of $F_g = G \frac{m_1 m_2}{r^2}$; the ...
2
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2answers
884 views
Angles on swing sets
I'm building a swing set for my children. All of the designs I've seen involve building two A-frames and connecting them at the top with a crossbar/beam from which hang the swings. The A-frames are ...
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5answers
977 views
Why Gravity attracts all objects with the same speed?
Why Gravity attracts all objects with the same speed? Is this question was solved? What is the exact answer?
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2answers
101 views
Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$
Can someone please explain how this equation is valid, using intermediate steps if available?
$$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$
...
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1answer
118 views
Determining Orbital Velocity
Is there any way to determine the orbital velocity of a point around another stationary point, if I don't know the mass of either of the points but know the force that gravity exerts and the distance ...
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1answer
164 views
What controls whether a ball will skid or roll?
A billard ball is struck with a cue. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity $v_0$ of the ball, its radius $R$, its mass ...
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3answers
350 views
Can an object move without relying upon Newtons third law?
Pretty much everything we do appears to boil down to practice of Newton's Third law.
Even this rug I'm seated upon relies upon reaction from the floor to keep me seated. Amongst others the same ...
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2answers
182 views
From where does the force/energy of action-reaction comes from? (Newton's Third Law of Motion)
I was wondering, from where does the opposite force and thus energy comes from when we apply force.
For example, lets say there are two persons (P1 and P2) on the universe, and no force is applied to ...
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4answers
201 views
Is this a valid understanding of Newtonian mechanics?
This is a conceptual understanding of Newtonian mechanics. What the laws mean, how we know they're true, etc. I'm looking for criticism. I know this is really border line on the "don't ask questions ...
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2answers
53 views
Can you launch an item farther by slamming into it or accelerating it along a length
I am trying to desgin a little penny balista toy (built with a 3d printer).
The short description is that there is a track with a mass ("hammer") that slides along it. There is a stack of pennies in ...
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1answer
289 views
Acceleration of a Free-Falling System with Center-of-Mass Change
A thought experiment has been bothering me. Assume an enclosed box free-falling in a constant gravity field. The box contains a person and a bowling ball at the top end. The person throws the bowling ...
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1answer
319 views
Glass - paper: Stevin's Law
In my understanding the well-known experiment of the glass full of water in equilibrium with a piece of paper, the atmospheric pressure acts on a small layer inside the glass (on the top) and under ...
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1answer
197 views
Is my understanding of the mechanics of skidding correct?
I'm trying to understand the mechanics which determine if a car making a turn will skid.
Are the following correct or incorrect:
A vehicle making a turn will skid unless the centripetal force is ...
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3answers
190 views
How to imagine the following power and torque?
I can roughly feel a force of 10 newton only by considering the weight of 1 kilogram object.
How to imagine the following measurements?
Maximum horsepower 16 hp @ 9,500 RPM
Maximum torque ...
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2answers
94 views
Really basic mechanics and Galilean Relativity question
Consider two solid objects: A and B.
System 1:
A <----- B
10m/s
System 2:
A -----> B
10m/s
...
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1answer
345 views
What causes a force field to be “nonconservative?”
A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference.
Most force fields in physics ...
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1answer
146 views
How do I factor in multiple forces into these Newtonian mechanics equations?
Say a person is walking along.
He then jumps.
The person weighs $25$kg (irrelevant?).
Just after jumping, his velocity is 5m/s (positive is taken as up).
Gravity is taken as ...
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1answer
157 views
Why ballasted gliders fly faster
The fact:
Gliders have ballast tanks that can be filled with water. The addition of ballast increases weight, and this allows the glider to fly at faster airspeeds while maintaining the same glide ...
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3answers
434 views
What is the principle behind centrifugation?
What is the principle behind centrifugation?
I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system.
However I don't quite ...
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3answers
80 views
Estimate quarter mile time
I need to estimate a drag race quarter mile time given the car's weight, bhp and preferably the drive (FWD, RWD, 4WD). I know $v(t) = ds/dt$ and $a(t) = dv/dt = d^2s/dt^2$, but how can I get the ...
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3answers
597 views
Why airplanes fly: the final truth
The questions about the reasons the aircraft fly are frequent among scientist, since the high school until now, even if I work on the other side of fluid mysterious world (the Low Reynolds numbers ...
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0answers
107 views
A problem on mechanical energy and friction
I'm studying for a mid-term, and I'm trying to solve some mock-papers. The following are two problems which I have solved, but I'm missing a part:
$(1)$ A body of mass $ m_1= 8 \rm kg$ passes ...
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2answers
213 views
The two-body problem: What is force between them?
Two bodies with similar/different mass orbiting around a common barycenter.
What is force between them, where $F_{12}$ is the force on mass 1 due to its interactions with mass 2 and $F_{21}$ is the ...
2
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1answer
192 views
When does centripetal force cause constant circular motion?
As far as I know, if an object has a speed $s$ and a force is applied to it which generates an acceleration of $s^2/r$, then the object will start moving in a circle of radius $r$. Also, as far as I ...
2
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1answer
126 views
Snooker/billiards cueing
I understand the 2 body dynamics very well, but I can't see how the professionals apply their chalked cue and hit the way they do.
As a few for instances:
How much does the chalk come into play in ...
2
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1answer
350 views
Circular Motion Equation Derivation
I am given a series of three equations, which someone has used to determine the Tension force in a rope swing:
$$mgh=1/2mv^2$$
$$T-mg=\frac{mv^2}{r}$$
$$T=3mg=1764N$$
I am asked to exaplain the steps ...
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2answers
289 views
Why didn't Newton just propose the 2nd Law and leave it at that?
Why didn't Newton just propose the 2nd Law ($F=\dot{p}$) and leave it at that? The 2nd Law implicitly contains the first, doesn't it? If so, it seems he wasn't following his own Rule #1 of Book 3 of ...
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1answer
96 views
Gravitation and equilibrium (…and similar problems)
One problem that I'm having trouble with (as opposed to the other):
The Messenger is a probe that orbits Mercury $700 \rm km$ from the surface. What is the tangential velocity it should be ...
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1answer
99 views
Storing light energy as potential kinetic to drive an electric generator [closed]
I would like to lift a 10 ton mass (crate of rocks) to a height of about 80 feet using a small 24 volt electric motor powered by a 16 square foot photovoltaic panel. Then I would like to collect the ...
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1answer
261 views
Analogy between magnetic bottle and Van Allen's radiation belt
A magnetic bottle is an arrangement that permits to confine charged particles. Here you can find a review for charged particle rotating in a magnetic field and at the bottom of the page a description ...
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2answers
896 views
Circular motion period equation
The equation,
$$ a_c=\frac{4\pi^2r}{T^2} $$
Can be expressed as:
$$ F_c=\frac{m4\pi^2r}{T^2} $$
I am confused as to how to arrive at this second equation, and the relationship between these two ...
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2answers
217 views
At what g is terminal velocity not terminal?
How weak would gravity need to be in order for a human to reliably survive the terminal velocity of falling through air?
(Context: watching scifi on a space station with a variety of artificial ...
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2answers
128 views
Unexpected potential energy increase during Tic-Tac drop
I dropped a Tic-Tac:
(no worries, it happened before), and I noticed as it bounced on the floor that it would first jump 20 cm high, and at the next bounce for instance 50 cm high. Shouldn't it ...
5
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1answer
202 views
What in Newtons three laws of motion original to himself and not a paraphrasing of his predecssors
The three laws are:
First law: The velocity of a body remains constant unless the body is acted upon by an external force.
Second law: The acceleration a of a body is parallel[disambiguation needed ...
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2answers
887 views
Determine the acceleration and angular acceleration of a disc
The question is:
A 90kg disc is floating in a frictionless vacuum. A 150N force is
applied to the outer rim of the disc. The disc has a radius of 0.25m
and a radius of gyration of 0.16m. What ...
2
votes
2answers
494 views
Why is the center-of-mass of 2 bodies at the focus of their elliptical orbits?
Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?
I know that when there are no external forces, the center of ...
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5answers
363 views
Does Newtonian mechanics predict the bending of the course of light by objects with mass?
$F=Gm_1m_2/d^2$
$F=ma$
$a_g=Gm_{other}/d^2$
In Newtonian mechanics, the acceleration of object A toward object B is not dependent on the mass of object A but on the mass of object B and the ...
2
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4answers
545 views
How long must escape velocity be maintained?
Escape velocity from Earth's surface is 11.2 Kilometres/second
How long would one need to maintain this escape velocity to actually escape Earth's gravitational pull? Must this 11.2 km/s velocity ...
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0answers
96 views
Hooke's Law and the shape of coils
I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions:
Is it always linear for every shape of a coil? Does it remain linear if we ...
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3answers
828 views
Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$
A problem I am trying to work out is as follows:
A particle moves in a force field given by
$\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant.
...
2
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1answer
159 views
What is the Lie algebra of the Galilean group and what is the structure of it?
I read Freeman Dyson's article Missed Opportunities, in which he talked about the mathematical attractiveness of the Lorenz group compared to the Galilean group. I am reading Florian Scheck's book on ...
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0answers
182 views
The Gravity Spring [closed]
This problem examines the scenario of a tunnel drilled through the center of the Earth, and the length of time required for an object to fall through the hole and back again.
use trigonometry to ...
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3answers
849 views
Does friction decrease as objects move faster against each other?
I was told that the faster two objects move against each other, the less the friction between them would be… compared to if they were moving slower. In physics class, we always use the coefficient of ...
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1answer
68 views
How do we describe the relationship of balloon size and related lift?
We know that hydrogen and helium are lighter that air.
Therefore it is certain that they would create a lifting force when enclosed in a balloon.
How do we describe the relationship of balloon size ...
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0answers
55 views
Two particles rest [closed]
Two particles rest a distance $d$ apart on the edge of a table. One of the particles, of mass $m$, falls off the edge and falls vertically. Using the other particle (still at rest) as the origin, ...
