Newtonian mechanics Definition and 124 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.
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...
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...
$$ R - f = m\ddot x$$ $$N - mg = m\ddot y$$
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...
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...
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 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...
Homework Statement
The problem is in attached screenshot. Now,I solved this using force/torque method. However ,I got different solution as given in solution manual. Where I have gone wrong?
Homework Equations
The Attempt at a Solution
Applying F=ma to cylinder:
$$mg-T=ma$$
Applying ##\tau...
Homework Statement
This problem was originally posted on Physics Problems Q&A: http://physics.qandaexchange.com/?qa=616/friction-between-two-disks
Homework Equations
Second Newton's law for rotation:
$$\tau = I \alpha = RF$$
The Attempt at a Solution
I tried to solve this problem as...
Homework Statement
You buy a bottle of water in the store and place it on the conveyor belt with the longitudinal axis perpendicular to the direction of movement of the belt. Initially, both the belt and the bottle are at rest. We can approach the bottle as one cylinder with radius ##R##, mass...
Homework Statement
[/B]
A train stands in the middle of a rotating disk with an initial angular velocity of
$\omega_i$. The mass of the train is m and the moment of inertia of the train-disk is I. At one point the train departs on a straight track to a distance R from the disk's centre. (R...
Homework Statement
A weight is suspended from a spring 50 cm long and stretches it by 1 cm. Take the other end of the spring in your hand and rotate the weight in a horizontal plane so that the spring is stretched by 10 cm. What is the velocity of the weight? (The force with which the stretched...
1. Homework Statement
A 60 kg block is pushed horizontally with just enough force to start its motion Accross a floor and the same force acts on it afterwards.The coefficient of static and sliding frictions are 0.5 and 0.4 respectively.
Find acceleration of the body.
Options
6m/s^2
4.9m/s^2...
What makes frictional force the centripetal force of a car turning along a curve?
As friction is the opposing force and acts anti-parallel so there is no component of frictional force towards the center,right? Then how can frictional force be centripetal force?
Many books sometimes for example define energy as quantity and sometimes as property. Also the definition of energy is the ability to do work or the meter of the ability to do work ? we define for example force as a quantity or as some quality and then we quantify this ?
For example F=ma means that the definition of force is m*a or the quantity of left side equals to the quantity of right side or both ? or kinetic energy..we know K=1/2mu^2 but is this the definition of kinetic energy or just the formula to calculate it ?
A particle of mass m in xy plane is attracted toward the origin with the force
$$\begin{align}\vec{f} = - \frac{k^{2} m}{r^{6}}\vec{r}\end{align}$$ where ##\vec r## is position vector of particle measured from origin. If it starts at position ##(a,0)## with speed $$v=\frac{k}{\sqrt{2} a^{2}}$$...
Homework Statement
A professional thrower projects a football straight up in the air.
1. Assuming there is no air drag on the football, find the speed of the football as a function of height as the ball goes up.
2. Assuming the air drag on the football varies linearly with speed, find the speed...
The situation:
The mass is pushed up an incline with an angle of 1 degree with an initial velocity of 1 m/s, and it comes back down to its original position.
The questions to answer:
What is the total distance the object travels on the frictionless inclined plane?
How long will the object...
Homework Statement
A bead slides under the influence of gravity on the frictionless interior surface of the paraboloid of revolution z = (x^2+y^2)/2a = r^2/2a Find the speed v_0 at which the bead will move in a horizontal circle of radius r_0 Find the frequency of small radial...