In physics, motion is the phenomenon in which an object changes its position over time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and time. The motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without reference to its cause is kinematics; the branch studying forces and their effect on motion is dynamics.
If an object is not changing relatively to a given frame of reference, the object is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be in motion.Motion applies to various physical systems: to objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time. One can also speak of motion of images, shapes, and boundaries. So, the term motion, in general, signifies a continuous change in the positions or configuration of a physical system in space. For example, one can talk about the motion of a wave or about the motion of a quantum particle, where the configuration consists of probabilities of occupying specific positions.
The main quantity that measures the motion of a body is momentum. An object's momentum increases with the object's mass and with its velocity. The total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum. An object's motion, and thus its momentum, cannot change unless a force acts on the body.
A water molecule is as tiny as 0.3 Angstrom. I would expect that quantum effects play a role. I'm wondering if its Brownian motion in a fluid is determined only by classical thermodynamics or if its collisional processes must take into account also quantum scatterings or other effects like...
I am trying to understand the differences in design between a traditional solenoid with a ferrous plunger vs linear motors that use either induction or permanent magnets. From my understanding, a traditional solenoid, whether DC or AC, cannot fire in both directions with polarity switching since...
Hi guys,
I can't seem to be able to get to
$$ (\rho + p) \frac {d\Phi} {dr} = - \frac {dp} {dr} $$
from
$$T^{\alpha\beta}_{\,\,\,\,;\beta} = 0$$
the only one of these 4 equations (in the case of a spherically symmetric static star) that does not identically vanish is that for ##\alpha=r##...
I have been trying to solve the following problem:
Point-like object at (0,0) starts moving from rest along the path y = 2x2-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j. a) Find the work done by F along the path, b) Find the speed of the...
TL;DR Summary: I want to mainly figure out where in the problem solving I went wrong. I understand the correct answer (since I looked it up), but to me, it does not make any sense.
I am honestly stumped at this point. Online solutions say that my equation y = 0.5774x-0.003354x^2 should...
Here is a picture of the problem
It is not clear to me how to really prove that the equation for ##\theta(t)## is simple harmonic motion, and what the period of this motion is.
Can someone show that the instantaneous circle is indeed given by when the centripetal force is removed?
This can be found at https://www.vedantu.com/iit-jee/circular-motion
The answer key states that the new tangential speed is half the original speed. However, this isn't correct right? It should double.
My proof:
##F_c = \frac {mv^2} R##
##F_c = F_t##
##\frac {mv^2} {\frac R 4} = \frac {m(2v)^2} R## If centripetal force were to stay constant.
As such, tangential...
(Please refer the image below. ) The velocity of Nick ##v_N=\omega r## and the velocity of John ##v_S=\omega R## is depicted. The relative velocity of Nick with respect to John will be ##v_{NJ} = \omega (R-r)##. The velocity is along the tangent to the circle centred at B. If Nick were to move...
Hello Everyone
I want to model forces affecting on syringe plunger , but I do not know how to calculate terms like friction and damping coefficient.
What I imagine is that : F_driving = ma + cv + f ----------------(1)
where:
f: friction
c: coefficient of viscous damping
m: mass of plunger (is...
As you all know, a bungee jump is where a person is tied to a cord and the person jumps off and bounces up again.
The natural length of a cord is 75 metres. Then when a person is attached onto the cord, the length becomes 83 metres when the person is at rest. I am sure that the person is not...
Initial displacement is h above the ground ie ##s\left ( t =0\right )=h##. I've chosen the ground as the vertical origin with upwards as the positive direction. Gravity will therefore always act in negative direction throughout. Here are the graphs I which to reproduce from first principles...
Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2.
The ship is accelerating the first half of the trajectory and decelerating the second half.
I calculated the velocity profile from the Earth reference:
The travel time on...
According to Chapter 8 of Griffiths' book Introduction to Electrodynamics, the magnetization force that acts on a magnetic dipole is
$$F_M=\nabla (m \cdot B)$$,
where ##m## is the magnetic moment and ##B## is the magnetic field.
For a paramagnetic or diamagnetic particle...
Hello everyone!
I was wondering about this physics problem.
First example:
If a rocket is traveling in a straight line continuously in uniform motions from position 0 to position 1000 in 10 seconds then it will move through an infinite number of points.
Since it is always changing position...
The system is shown below. It consists of a rod of length ##L## and mass ##m_b## connecting a disk of radius ##R## and mass ##m_d## to a collar of mass ##m_c## which is in turn free to slide without friction on a vertical and rigid pole. The disk rolls without slipping on the floor. The ends...
I am not understanding the 2nd part of the question where it is asked about how many revolutions will the blade make when it reaches full speed. Please help
For part (a) and (b) of this problem,
The solution is,
However, how did they arrive at their conclusion in part(b)?
As you can't graph it on a GC, I decide to imagine plugging in values for t, which I see that the 2t^3 grows quicker than the t^2 which is why I think they said that the...
My reasoning was to use this kinematic equation to first get time of flight of the baseball using horizontal components, and then use this same equation again to find initial velocity.
i,j,k arevector
I know L=P*r=m*v*r=m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k=mabωk.
but why m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k.I need some detail.
please help me.
F parallel - F applied - rolling resistance = ma
I don't know how to calculate for rolling resistance. If the bicycle is not slipping rather it is rolling, should I ignore rolling resistance? And if I ignore that I would get,
F parallel - F applied = ma
F applied = F parallel -ma...
Alice rests at ##X=L+1## in the inertial frame (T, X).
Bob is at rest in the Rindler frame (t, x) at ##x=1## and has the proper acceleration ##\alpha=1##.
In the rest frame of Alice, Bob moves from event ##E_1=(-T_2, L+1)## over the distance of ##L## in negative X-direction to event ##(0, 1)##...
I am looking at a textbook solution to the following problem of finding the equation of motion of a half disk. In the solution, the author considers the half disk has a COM at the black dot, and to find the instantaneous translational velocity of the center of mass (he considers rotational...
Good morning, I'm not a student but I'm curious about physics.
I would like to calculate the equation of motion of a system using the Lagrangian mechanics. Suppose a particle subjected to some external forces.
From Wikipedia, I found two method:
1. using kinetic energy and generalized forces...
A V-shaped tube with a cross-section A contains a perfect liquid with mass density and length L plus and the angles between the horizontal plane and the tube arms as shown in the attached figure.
We displace the liquid from its equilibrium position with a distance and without any initial...
We know the time it takes the water complete the whole parabola is (sin(x) * 6.5 * 2) / 9.8.
So I come up with (sin(x) * 6.5 * 2) / 9.8 * cos(x) * 6.5 = 2.5, because the x component of the velocity is the same for the whole time.
But I get the results like these: x≈0.30929171+πn,1.26150461+πn...
I worked myself into a trigonometry rut. I've tried two approaches, first by not changing the frame of reference, and second by taking the incline as the horizontal x axis. Here is my second attempt:
Take the incline as the horizontal. Then the coordinates of target T are:
$$
\begin{align}
x_T...
t=0 => v(0) = 4(0) - 3(0)^2 = 0m/s
t=2 => v(2) = 4(2) - 3(2)^2 = -4m/s
Vavg => (v(0) + v(2))/2 = -2m/s
When researching the answer, I noticed that they used integrals to solve this question. The only problem is that we never learned about integrals/ derivatives or anti derivative. Is there any...
From the equation for centripetal force, I can see that the centripetal force is proportional to v^2. Does this have something to do with why there is a normal force at the top? Does the velocity of the object require there to be a normal force? If so, why is that the case?
If we have charged particles having Brownian motion, would this motion be associated with (or produce) heat or electricity? Would it produce electromagnetic radiation (and if it would produce it, what type of radiation in the electromagnetic spectrum)? Could there be Brownian motion of charged...
After 3,32 seconds, vt should have varied by 0,695*3,32. I have done a previous exercise where you only needed to calculate the radial acceleration in this scenario. There, I took the vt after the given time, squared it and then divided with the radius. I remember clearing that one, so in this...
Hi, I have a question about the motion of a charged particle in crossed E and B fields. if B was pointing in the Z direction and E in the y direction then the component of the motion in the Z plane = 0. The only reason for this to happen is that the electric force due to the E field depends on...
I was reading Mechanics by Landau and Lifshitz and I am confused when it is stated in chapter 2 section 6 that one of the integrals of motion is not independent and it can be considered an additive constant of time. Hence I tried searching it up online...
Summary: I am just trying to go through a Brilliant physics unit. I came across this axe throwing question which I don't get at all how they get the answer.
You can see the answer there.
So their explanation is;
'In going around the circle, the red point moves through an angle of
θ =...
The speed of a wave in simple harmonic motion on a string is $$v= \sqrt{\frac{F}{\mu}}$$ where v= the horizontal velocity of the wave on a string.
Is the F the horizontal force or the resultant force (combination of Fy and Fx)?
The question is solved in a single step by taking the blocks as a system and using conservation of linear momentum in the horizontal direction as there is no net force acting in the horizontal direction.
Conserving the momentum we get,
m x v + M x 0 = (m+M)v',
so,,v' = mv/(m +M).where v' is the...
The Lagrangian for a massless particle in a potential, using the ##(-,+,+,+)## metric signature, is
$$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,$$
where ##\dot{x}^\mu := \frac{dx^\mu}{d\lambda}## is the velocity, ##\lambda## is some worldline parameter, ##e## is the auxiliary einbein and...
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...
In the holonomic case, we can put the Lagrangian in the Lagrange equations to obtain the explicit form of the equations of motion. From Greenwood's classical dynamics book, the equations are
Are there such general equations for the non-holonomic case?
While solving this question I could not figure out the concept of two blocks sticking together.
the question is,
Two particles A and B of masses 1 kg and 2 kg respectively are projected in the directions shown in figure with speed uA =200m/s and uB =50m/s. Initially they were 90m apart. They...