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.

learn more… | top users | synonyms (2)

5
votes
15answers
11k views

Recommendations for good Newtonian mechanics and kinematics books

What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.?
51
votes
15answers
12k views

Why does kinetic energy increase quadratically, not linearly, with speed?

As Wikipedia says: [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $mv^2/2$. Why does this not increase linearly with speed? Why does it take so much ...
42
votes
8answers
17k views

Why does the atmosphere rotate along with the earth?

I was reading somewhere about a really cheap way of travelling: using balloons to get ourselves away from the surface of the earth. The idea held that because the earth rotates, we should be ...
3
votes
3answers
1k views

If it was possible to dig a hole that went from one side of the Earth to the other…

...And you jumped in. What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like ...
10
votes
12answers
4k views

Why do we say that the earth moves around the sun?

In history we are taught that the Catholic Church was wrong, because the Sun does not move around the Earth, instead the Earth moves around the Sun. But then in physics we learn that movement is ...
13
votes
3answers
858 views

Are Newton's “laws” of motion laws or definitions of force and mass?

If you consider them as laws, then there must be independent definitions of force and mass but I don't think there's such definitions. If you consider them as definitions, then why are they still ...
4
votes
5answers
1k views

Why do two bodies of different masses fall at the same rate (in the absence of air resistance)?

I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time. According to Galileo, two bodies of different masses, ...
28
votes
5answers
9k views

With Newton's third law, why are things capable of moving?

I've got a rather humiliating question considering newton's third law "If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A" -> $F_1=-F_2$ ...
15
votes
4answers
566 views

Anti-gravity in an infinite lattice of point masses

Another interesting infinite lattice problem I found while watching a physics documentary. Imagine an infinite square lattice of point masses, subject to gravity. The masses involved are all $m$ and ...
18
votes
2answers
2k views

History of interpretation of Newton's first law

Nowadays it seems to be popular among physics educators to present Newton's first law as a definition of inertial frames and/or a statement that such frames exist. This is clearly a modern overlay. ...
6
votes
3answers
3k views

A fly in an accelerating car

A fly is flying around in a car, the fly never touches any surface in the car only fly’s around in the air inside the car. The car accelerates. does the fly slam in to the rear window. or does the fly ...
26
votes
10answers
10k views

How did Newton discover his second law?

I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to ...
8
votes
6answers
1k views

Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?

For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$ \frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$ From this, it ...
10
votes
3answers
471 views

infinite grid of planets with newtonian gravity

Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving ...
11
votes
2answers
2k views

Are there examples in classical mechanics where D'Alembert's principle fails?

D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero. This is obviously true for the ...
3
votes
3answers
2k views

Why I think tension should be twice the force in a tug of war

I'm going to provide my argument for why I think the tension in a rope should be twice the force exerted on either side of it. First, let's consider a different example. Say, there is a person named ...
8
votes
4answers
2k views

Dependence of Friction on Area

Is friction really independent of area? The friction force, $f_s = \mu_s N$. The equation says that friction only depends on the normal force, which is $ N = W = mg$, and nature of sliding surface, ...
7
votes
2answers
2k views

Explanation that air drag is proportional to speed or square speed?

A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the drag (air resistance) which is proportional to the object's speed. By Newton´s laws this can ...
15
votes
6answers
12k views

Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?

I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ...
4
votes
2answers
883 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 ...
1
vote
1answer
298 views

Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
6
votes
5answers
8k views

Why does a ballerina speed up when she pulls in her arms?

My friend thinks it's because she has less air resistance but I'm not sure.
2
votes
1answer
6k views

Torque Required For a Motor to Move an Object on Wheels?

I've been attempting to calculate how much torque a motor needs to produce in order to start a stationary object on wheels moving. (The torque is being applied to the rear 2 wheels, the front 2 are on ...
11
votes
8answers
4k views

How do you explain spinning tops to a nine year old?

Why don't spinning tops fall over? (The young scientist version) My nine year old son asked me this very question when playing with his "Battle Strikers" set. Having studied Physics myself, I am very ...
6
votes
3answers
2k views

How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?

The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a ...
18
votes
4answers
682 views

How can I determine whether the mass of an object is evenly distributed?

How can I determine whether the mass of an object is evenly distributed without doing any permanent damage? Suppose I got all the typical lab equipment. I guess I can calculate its center of mass and ...
1
vote
2answers
685 views

Force applied off center on an object

Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. ...
7
votes
4answers
704 views

Rotation of a slipping ladder

Imagine a ladder leaning against a wall. All surfaces are smooth. Hence the ladder will slip and fall. While falling it rotates because there are external torques acting on it. My question is about ...
13
votes
4answers
1k views

Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
11
votes
3answers
2k views

Galilean invariance of Lagrangian for non-relativistic free point particle?

In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian $$L = \frac{1}{2} mv^2$$ for a non-relativistic free point particle is ...
9
votes
1answer
5k views

Derivation of the centrifugal and coriolis force

I was wondering how easily these two pseudo-forces can be derived mathematically in order to exhibit a clear physical meaning. How would you proceed?
5
votes
4answers
1k views

Logical connection of Newton's Third Law to the first two

The first law and second laws of motion are obviously connected. But it seems to me that the third law is not related to the first two, at least logically. (In Kleppner's Mechanics the author states ...
16
votes
8answers
5k views

Why don't spinning tops fall over?

One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't ...
14
votes
2answers
1k views

Norton's dome and its equation

Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$. Via Norton's web. If we put ...
-5
votes
4answers
686 views

Violation of Newton's Second Law (?) [closed]

Here the big circle denotes the circular path of a stone (small circle on path) tied to a string from the centre of the circular path. This is COMPLETELY HORIZONTAL At an instant the velocity in ...
8
votes
2answers
496 views

Huge buildings affect Earth's rotation?

Does constructing huge buildings affect the rotation of the Earth, similar to skater whose angular rotation increases when her arms are closed comparatively than open?
5
votes
1answer
600 views

Kepler problem in time: how do two gravitationally attracting particles move?

Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ ...
5
votes
3answers
1k views

How do the Planets and Sun get their initial rotation?

How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets and why does Venus rotate in a different direction to Mercury, Earth and ...
3
votes
1answer
4k views

Two masses attached to a spring

I'm trying to understand the solution of the following problem. Two masses $m_{1}$ and $m_{2}$ slide freely in a horizontal frictionless track and are connected by a spring whose force constant is ...
2
votes
2answers
342 views

Angular momentum of a translating and rotating body

If a rod is rotating about one end, does it have pure rotation or do you also consider the translation of centre of mass when calculating its angular momentum? Also, how would one calculate the ...
1
vote
1answer
318 views

Newtons Cradle, Collision Theory

It has come to the point in my computing program now where I have 5 swinging pendulums that are all modified at once by slider values. These values are drawn onto the from and passed through the class ...
0
votes
2answers
1k views

What will be the relative speed of the fly? [duplicate]

It has happened many times and i have ignored it everytime. Yesterday it happened again . I was travelling in a train and saw a fly (insect) flying near my seat. Train was running at a speed of ...
-1
votes
2answers
416 views

Two balls falling one above the other [closed]

Two balls, first with the mass $m_1$ and the second with the mass $m_2$ are falling from the heigh $h$. Suppose all the collisions are perfectly elastic and do not consider the size of the balls. $m_1 ...
57
votes
7answers
4k views

Does juggling balls reduce the total weight of the juggler and balls?

A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that ...
17
votes
7answers
9k views

What is the difference between Newtonian and Lagrangian mechanics in a nutshell?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the ...
25
votes
4answers
9k views

What are the precise statements by Shouryya Ray of particle dynamics problems posed by Newton which this news article claims have been solved?

This recent news article (here is the original, in German) says that Shouryya Ray, who moved to Germany from India with his family at the age of 12, has baffled scientists and mathematicians by ...
4
votes
4answers
434 views

Is Newton's first law something real or a mathematical formalism?

Why do objects always 'tend' to move in straight lines? How come, everytime I see a curved path that an object takes, I can always say that the object tends to move in a straight line over 'small' ...
9
votes
5answers
2k views

Is the energy conserved in a moving frame of reference?

Consider this situation: When the box is at the bottom of the frictionless incline, it will have a velocity of $v_f$. The person is an inertial frame of reference that moves at a constant ...
4
votes
3answers
734 views

An example of non-Hamiltonian systems

I am preparing for the exam. And I need to know the answer to one question which I can't understand. "Give an example of non-Hamiltonian systems: in case of infinite number of particles; for a finite ...
3
votes
2answers
706 views

Why are there both Static and Kinetic Friction?

When dragging an object, there is a greater start-up force than the force it takes to keep it moving. Why is this? Why are there two different values for friction?