Motion Definition and 999 Threads

If it were supposed that time were a 4th non-spatial dimension how would it influence the gravitational movement ? The problem I have when trying to solve this invented problem is that Newtonian physics works in coordinates and that there are a lot of ways to find 4d 3+1 hyperbolic-spherical...

I need help to understand this problem taken from Mechanical Vibrations by S. Rao I know that the equations of motion could be obtained in various ways, for example using the Lagrangian, but, at the moment, I am interested in understanding the method he used. In particular, if I'm not...

I know that I need to find the equation of the line of motion of the two particles, the dot product of which with one of the options will give 0. I began with founding the coordinates of center of mass: R = (m1r1+m2r2)/(m1+m2) = (2a/3, 0, a/3) and velocity of the center of mass: V =...

In the Schwarzschild metric case why is : $$r=cste,$$ $$\theta(t)=\arccos(\sin\alpha\cos\omega t)),$$ $$\phi(t)=\arctan(\tan(\omega t)/\cos\alpha),$$ $$t=\tau$$ not solution to the geodetic equation ?

Part (i) *Pink represents mark scheme method Part 2 However I am still confused on the diagram.

Why is my analysis of critically damped motion wrong? x'' + y*x' + wo²x = 0 Choosing a complex number z as z = A*e^i(wt+a) and putting on the equation calling x as the real part of Z w = ( i*y +- (4wo²-y²)^(1/2) )/2 (bhaskara) 2wo = y (critical) w = iy/2 z = A*e^i(ity/2 + a) z = A*e^(-yt/2...

Hey guys! I´m having a lot of trouble , even on starting this problem. Can someone give me a help?? [Moderator's note: Moved from a technical forum and thus no template.]

To get the velocity I integrate the accelaeration function and get v_0-c*(t_2-t_1)^2/2 since I think these should be the boundaries of the definite integral. Bu the correct answer is v_0-c*(t-t_1)^2/2 and they integrate from t (upper limit) to t1 (lower limit). Could you please help me to...

Greetings, I currently work my way through Langevin Dynamics which, in a certain limit, becomes Brownian Motion. I refer to this brief article on Wikipedia: https://en.wikipedia.org/wiki/Brownian_dynamics I understand the general LD equation given there. In order to obtain Brownian Dynamics...

its a short question...

Below is my working out. If you could have a look at my answers and see if they are correct and then advice me on how to improve my solutions for Parts I and II, and how to answer F and G with the given information. Thanks in advance! Parts aand b are diagrams so please refer to the attached...

Let me ask a very primitive question. To and fro motion of pendulum under gravity tells us potential energy + kinetic energy = const. At the top points potential energy: max kinetic energy :0 At the bottom point potential energy: 0 kinetic energy :max EM wave is usually illustrated as...

I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...

I need an equation to predict the flight path of a changing mass projectile under changing thrust. Any thoughts?

Let say the displacement of the first interval of 1 second is 10 m, so the displacement of the next 1 second interval will be 13 m, and the next after this one will be 16 m and so on. Option (a) and (b) are wrong because in any interval of 1 second the displacement will be constant I think...

Linear Motion Equation to get the common velocity of the block and bullet just after collision: v2=u2+2gs, I set v=0 at max height of s = 0.004 m and g = -9.81 m s-2 I got u = 0.28 m/s Then I calculate the impulse of the block using formula J = mv - mu, where v=0 and u=0.28 m/s and I got J = 1.4...

Hi. I'm not expert in physics. Recently I have written an article how a spacecraft will remain in orbit forever. However need review if there is any mistake using formulas or the term escape velocity. Here is it, Layman question: So what will happen if we use sci-fi spacecraft to takeoff...

Hello, I have a system with 2 degrees of freedom with 2 non-holonomic constrains that can be expressed by:##A_1 dq_1 +Cdq_3 + Ddq_4 = 0## ##A_2 dq_1 + Bdq_2 = 0##Being ##q_1, q_2, q_3## and ##q_4## four generalized coordinates that can describe the movement of the system. And ##A_1, A_2, B...

Could I please ask for help regarding the final part of the following question: It is the very last part, to find v in terms of u. So I have that the velocity of the midpoint of XY is: V_m = (u/2) i + (u/2) j I let the position vector of P be: r_p = cos(wt) i + sin(wt) j (w = angular...

This is diverted from the Classical Physics forum. My first approach was this: the force ##\vec{F}## can be written in polar coordinates as ##\vec{F} = F \hat{\theta}##. It follows that ##F_{\theta} = ma_{\theta} \implies F = m(2\dot{r}\dot{\theta} + r\ddot{\theta})##. This result also agrees...

I think i could deal with this problem interpreting this force like a central force, what seems pretty nice to me, since in a circular orbit the force will always pass through the center, if it is perpendicular to the velocity. I thought, since the force is central and in this case, spherically...

There's a constant magnetic field B. If a particle is acted on by a force qv*B (* cross) only, and the initial velocity v0 is normal to B, is the motion certainly a circular one (for any m, q, v0)? mv''=qv*B If one solves this equation (vector), it doesn't seem obvious.

A Problem is posed for a flight from Melbourne to Cairns. Using the formula for rotational speed at latitude - 1) The latitude of Melbourne is approx 38 degrees south with a rotation velocity of 820 miles/hr 2) The latitude of Cairns is approx 17 degrees south with a rotation velocity of 994...

This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...

Hi, I have a motor that i would like to rotate to a certain angle, in a controlled manner. During the movement, i want to update the final position I want to reach. The new updated function has to start with the same speed the initial function ended with I wan to find a function that does this...

This is how I understand the torque (T1) created at the axis of rotation due to the spring would be calculated. This is considering the spring is starting from a fully extended state and is not already compressed. This is considering that (A) has a distance of 2 in. and the force from the spring...

Hello, For a motor, we need to calculate the traveled distance and proper timing for its motion. Here is the trapzodial motion of our motor( we need that our motor traveled 20 degree in 2 seconds). (where t2=2t1) we know that the traveled distance is surface of our velocity diagram. So...

First of all, i know that the motion will be bounded, is not necessary to know if the motion will be closed or not. Second, by analyzing the graphic of a effective potential with such conditions, the motion will agree with harmonic motion. Ok I don't know how to prove the harmonic oscillation...

Very confused at this. https://courses.lumenlearning.com/physics/chapter/10-6-collisions-of-extended-bodies-in-two-dimensions/ "Consider the relatively simple collision shown in Figure 2, in which a disk strikes and adheres to an initially motionless stick nailed at one end to a frictionless...

The equation of motion can be integrated w.r.t. ##t## since ##\frac{d}{dt} (\mathbf{r} \times \mathbf{B}) = \dot{\mathbf{r}} \times \mathbf{B} + \mathbf{0}## $$\int (q\dot{\mathbf{r}} \times \mathbf{B} + m\mathbf{g}) dt = \int m\ddot{\mathbf{r}}(t) dt$$ $$\frac{q}{m} \mathbf{r} \times \mathbf{B}...

I am at my wits end with trying to find this formula. So far all I've gotten is I need to figure out mechanical power, maybe torque? I can't figure out the formula for this motion as it is like negative leverage. I want to build a machine that can do this thousands of times so I also need to...

Hi everyone, I need help for this homework. I'm a mechatronics engineering student and i want to solve this question but no matter how hard I try, I can't solve the question. Sorry for my bad english...The disk connected to the AB stick with a length of 2 meters is rolled as shown in the figure...

this is problem #57 from chapter 4 of "Physics for engineers and scientists vol1" ,it was solved in the book by a method the author calls "successive approximation, he first calculated the flight time of the projectile and then "corrected" for the ship's displacement. i know this is a perfectly...

Hey guys, Theres something I've been confused about when looking at circular motion. When does an object have just centripetal acceleration as the acceleration of the object, if ever. I think that the acceleration vector is between the centripetal and tangential acceleration when an objects...

https://www.physicsforums.com/attachments/262043I got here, i think that the component y N will balance the mg force; the other componente of N will be divided in two, one to balance the force, and other to be the centripal result, but i don't know how relate to each other

This is how I think the set up of the lab should look like. I've decided the height to be y=1,5m. The length x is assumed to be 0.32m. where Voy =0m/s the time it takes for the marble to drop 1,5m is 0,55s the inital velocity of the marble is around 0,47m/s I Think I have the...

Completely new to this and wondered if someone can explain what the correct equation of motion is if x is extension, t is time and a,b are constants x = b log (at) x = a t exp(-b t) x = exp(-b t) sin(a t) x = a sin(t)/b

Once I know the Hamiltonian, I know to take the determinant ##\left| \vec H-\lambda \vec I \right| = 0 ## and solve for ##\lambda## which are the eigenvalues/eigenenergies. My problem is, I'm unsure how to formulate the Hamiltonian. Is my potential ##U(r)## my scalar field ##\phi##? I've seen...

Diagram for question 2: Please check if my work is correct. Main equation: Fc = Fg - Fn Fn = Fg - Fc I assume that: Fn = Fg when stationary Fg = mg I divide by 5 because the apparent weight must be one fifth of her weight when stationary Fg = mg / 5 Fn = Fg Fn = mg / 5 Now to substitute...

Diagram for question 1: I know the mass, I need Fg. My work: Main equation: g = Fg/m I need to find Fg. Fg= Fc - Fn [Fn = 21 N Fc = ?] {I need to find Fc.} Fc = ma --> Fc = (mV^2)/ r [Mass = 1.3kg V = ? r = 0.70] {Now I need the velocity at that point where Fn = 21 N (the top of the...

This problem fascinated me in lower division physics. Find the 2-d equations of motion for a Slinky going down a flight of stairs (assuming the path of the slinky is planar; eg only going up and down and front and back, no side to side). I do confess that whilst I do love physics I’m not...

From my understanding the the distance of the two at time t would be 0. Because at the statement it is said that both objects start at the origin. To me the two expressions mean the same if both objects start at the origin I don't see how it matters what value is assigned to t.

I am not really sure how to go about this. I have been sick for a couple of weeks and fallen behind a bit. Can anyone help me out please? Thank you

Friction provides the necessary torque for rolling without slipping.So Rotational Energy must increase.Simultaneously acceleration of centre of mass down the inclined plane is positive so Translational energy also must increase.Overall The Gravitational Potential Energy is getting converted to...

**I realize some of my inline math delimiters '\(' and '\)' are not acting on the text for some reason, and it looks clunky. I spend 20-30 minutes trying to understand why this is, but I can't. My limited LaTeX experience is in Overleaf, and these delimiters work fine in that compiler. My...

a) Here I used the definition of current (reference: Tong notes, page 14) $$j^{\mu}_{\nu} = \frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi_a )} X_a (\phi) - F^{\mu} (\phi), \ \ \ \ \ \ \ \ \delta \mathcal{L} = \partial_{\mu} F^{\mu}; \ X_a (\phi) = \delta \phi_a$$ In our problem we...

If an analogy is drawn to kinematics problems in which for example a ball is thrown from a height h, when it strikes the floor it has a final velocity although it stops moving instantaneously. But in this problem, the points B and D have no linear velocity when E strikes the floor. Their final...

Here is the diagram of the problem: and here is the answer of the question: What I don't understand is equation 1 and 2. The Hook's law states that F = -k(change in x) Why the change in x1 equals to x1-x2+l? x1-x2 equals to the length of the compressed spring. I cannot convince myself that...