What is Newtonian mechanics: Definition and 204 Discussions
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond earlier works, particularly through their use of analytical mechanics. They are, with some modification, also used in all areas of modern physics.
Classical mechanics provides extremely accurate results when studying large objects that are not extremely massive and speeds not approaching the speed of light. When the objects being examined have about the size of an atom diameter, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. To describe velocities that are not small compared to the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. However, a number of modern sources do include relativistic mechanics in classical physics, which in their view represents classical mechanics in its most developed and accurate form.
So I’m a high school student and I am planing to participate in higher-category physics competitions in my country. However, I think that my theoretical understanding of the basics isn’t clear enough yet - by basics I mean classical / Newtonian mechanics. I am the type of person that learns by...
An alternative title could have been "how do forces propagate" but google searches bring up things related to waves only.
Initially my problems started with a mass on a spring but I was able to boil it down to any general system comprising at least two 'parts' in succession.
Suppose you have...
This isn't really a question per se, but it recently just 'clicked' for me and I would like to share what made that do so.
There are dozens of threads answering this question, but in my opinion most (but not all; there are some good threads on this forum, I just want to show how I came to...
I want to find a dimensionless value that differentiates between concentrated mass systems such as the solar system and dispersed mass systems such as a galaxy. I assume spherical and radial symmetry, consider both the cases for point masses or smooth mass distributions.
The only value I can...
I am having a difficult time finding papers that derive the equations of motions of the Restricted Three Body Problem using Newtonian mechanics. I have found some (barely) for the CRTBP, but there are none on the ERTBP.
Does it depend on what is being studied within the problem that the...
Hi, I’m making a vehicle simulator and I’m not entirely sure if my inertia calculations are right or are completely wrong. What I currently have now is something like this:
1. Engine:
engine_Out_Inertia = engine_Inertia; this should contain the inertia of the engine and all of it’s auxiliaries...
When you write out the equations of motion for a system of two isolated charges, you can add both of the equations and get the increase in the particles linear momentum on one side. On the other side, you get the sum of all the forces between the particles. I understand that this sum of forces...
I was thinking about how various objects would slide down on an inclined plane, and I just couldn't figure this problem out.
So let's say I have this screw or cone on its side, on an inclined plane. If friction exists, what would the motion of the screw be as it slides down the inclined plane...
My assumption says,as A moves to the right,there will be kinetic friction acting on it to the left and equal and opposite friction will act on B to the right,so it should move to the right keeping the center of mass go on moving with velocity mv/(m + M) to the right as there is no net external...
Static friction is known to provide centripetal force when a car turns.
Assuming uniform circular motion, my questions are
1. Is the static friction of each wheel points toward the center of turning circle or it's the combined forces of all four wheels that has to point toward the center of...
Hi, I am China Kang, a genius who once had no ambition and squandered green years. I started studying college physics in the summer of 2020. Nice to meet you all, and I hope to get your guidance.
Here is my depiction of the initial state:
Note that the presence of ##f_k## means the ball is initially slipping. We also know that the linear and angular speeds of the ball are increasing in time. At some point, the ball should stop slipping.
The condition for no slipping is that the speed...
In learning about translational and rotational motion, I solved a problem involving a wheel rolling down an inclined plane without slipping.
There are multiple ways to solve this problem, but I want to focus on solutions using energy.
Now to my questions. The reference frame in the posted...
I'm self-studying MIT OCW's 8.01, Introduction to Classical Mechanics Course. I am on the final week, where the topic is translational and rotational motion. I was following along the course notes and reached an example which I'd like to dive a bit deeper into, but I am not sure how.
The problem...
Show that a point with acceleration given by:
a=c*((dr/dt)×r)/|r|3
where c is a constant, moves on the surface of a cone.
This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that...
Image above is the question. Below image depicts solution.
if F1 is removed then the acceleration of that mass must be sum of accelerations of remaining forces. Right??
But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??
As the force on a pulley is equal to twice the tension, I just have to find the tension to solve part A. To do so, I first wrote the equations for both m1 and m2.
m1 * a = T - m1g
m2 * a = T + N - m2g
The tension must have the same values for both equations so I added both equations to find...
I've a disc which can rotate freely about two perpendicular axis (fixed to the body)
If I simultaneous try to rotate it about the two axis, what will happen?
Kleppner and Kolenkow say "Consider a gyrocompass consisting of a balanced spinning disk a light frame supported by a horizontal axle. The assembly is turntable rotating at steady angular velocity Ω. There cannot be any torque along the horizontal AB axis because the axle is pivoted".
I'm not...
I have attached two different attempts to solve this problem. They both look correct to me but they give two different answers! Which one is correct, which one is wrong and why?
What does it mean that the relationship between material mass and weight is constant and proportional?
Hi! Yes, another question... I have many doubts. :)
I hope someone can help me with this apparently very basic doubt, but I feel like a stupid monkey trying to join two sticks to reach bananas...
Consider the system of the mass and uniform disc.
Since no external forces act on the system, the angular momentum will be conserved. For elastic collision, the kinetic energy of the system stays constant.Measuring angular momentum from the hinge:
##\vec L_i = Rmv_0 \space\hat i + I \omega_0...
I have some difficulties in solving this problem. This is what I did.
I wrote down the equation of motion for the masses. For the first point
\begin{equation}
m\ddot{\textbf{r}}_1=\textbf{F}_1=q\dot{\bar{\textbf{r}}}_1\times...
Hello. The questions are: Why Newtonian mechanics is not applicable to quantum mechanics and more natural phenomena in gravity? So, we needed general relativity which offers a metric theory about gravity and applies to more phenomena in nature, but how is this explained that special and general...
$$ R - f = m\ddot x$$ $$N - mg = m\ddot y$$
were N and R are the normal reactions from the smooth wall and rough ground.
and f is the friction provided by the ground.
$$ f = \mu N = cot(\phi)N/4$$
i tried to formulate a constraint relation between ##\ddot x## and ##\ddot y## so that I could...
the point on the string at a distance r from the pivot is rotating in a circle of radius r and hence a centrifugal force of magnitude mw^2r can be said to act on it where m = (M/L)r .
hence the T = centrifugal force
T = (M/L)(wr)^2
but my book says otherwise.
also can the string with mass be...
Summary:: Would energy method give us a different answer from conservation of angular momentum?
Hello,
I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos.
Note: This question is not a homework. I did not find it in textbooks or...
FBD Block 1
FBD Block 2
FBD Pulley B
I'm mainly concerned with the coordinate system direction in this problem, but just to show my attempt, here are the equations I got from the system.
##-T_A + m_1g = m_1a_1##
##T_B - m_2g = m_2a_2##
##T_A - 2T_B = 0##
Using the fact that the lengths...
My attempt:
1) I am going to start this with a goal of setting up a reimann sum. First I divide the "arc"(?) of angle pi into n sub-arcs of equal angle Δθ
2) The total center of mass can be found if centers of mass of parts of the system are known. In each circular arc interval, I choose a...
I am learning to use polar coordinates to describe the motions of particles. Now I know how to use polar coordinates to solve problems and the derivations of many equations. However, the big picture of polar coordinates remains unclear to me. Would you mind sharing your insight with me so that I...
Situation: Let’s say we have a wire bent into a circular shape, there lies a bead through the wire and it can slide through it. The wire is kept in vertical plane and is swung along the axis AB.
My question : How the centripetal force is provided to the bead?
The bead will go into a...
Centripetal force is defined as the force causing the body to follow a curved path, acting towards the center and always orthogonal to the direction of motion. For uniform circular motion the formula for centripetal acceleration is $$a_c = \frac{v^2}{r}$$.
But my understanding of centripetal...
First we let the static friction coefficient of a solid cylinder (rigid) be ##\mu_s## (large) and the cylinder roll down the incline (rigid) without slipping as shown below, where f is the friction force:
In this case, ##mg\sin(\theta)## is less than ##F_{max}##, where ##F_{CM,max}## is the...
As you can see from the very last line of my post, this whole post may come from the fact that I don't get sarcasm o0)Hi, reading the above mentioned book I ran into the following footnote:
Postulate A was earlier stated as:
An alternative, but equal, version of Postulate A is given the page...
If a block slides down an inclined surface under the presence of the kinetic friction, does that mean the total energy lost by the block is equal to the work done by the kinetic friction? Thanks in advance.
I've solved this problem, I know you equal centripetal force with gravitational force, then rearrange for velocity to find T. My answer is the same as the one in the back of the book. But then I started thinking about it and don't know why they are equal to each other. Arent the forces in the...
I am having some difficulty understanding what "recoil" really is with respect to momentum, force, and and time.
On the one hand, momentum is considered to be the product of mass and velocity or perhaps the product of the sum of masses and some velocity, or some variant of P=mv, where P is a...
Hello,
I am having trouble understanding the two friction force terms from the ball rolling on page 4 of this physical model: http://www.dewtronics.com/tutorials/roulette/documents/Roulette_Physik.pdf
What is the reason for the cos\theta term ?
I think the frame of reference is made up of the...
In Newtonian mechanics, conservation laws of momentum and angular momentum for an isolated system follow from Newton's laws plus the assumption that all forces are central. This picture tells nothing about symmetries.
In contrast, in Hamiltonian mechanics, conservation laws are tightly...
If I can determine the weight of that heavy object placed on the plank, I will be able to determine the stretch of that wire. But, when using the second condition for static equilibrium (torques of the system equal to 0), I always end up with two unknowns, no matter what point of rotation I...
I am writing a paper for "Dynamics and statics" course. I am really interested in Graphene. I am not if this is a good topic for this specific course. Any suggestions? Thank you in advance
I attempted the solution using force method. I got correct. However, I was stuck at the alternative way to solve problem using energy method. As shown in screenshot 2, he tells that the energy of system changes due to 2 ways:
- The tension T
- Leaking of mass
As shown in screenshot 2 ,the...
Homework Statement
A boomerang is thrown with an initial linear velocity of 5 m/s at an angle of 30 degrees vertically. The initial angular velocity is ##2\frac{revolutions}{s}## At its peak, it has a displacement about the z axis of 2 meters and about the x-axis of 10 meters. The force applied...
Homework Statement
This is the problem 8.62(in screenshot) from Morin's textbook of Classical mechanics. I solved it using conservation of momentum in y direction. However in solution manual,he neglects the momentum in y direction by calling stick frictionless. What is this frictionless stick...