Dynamics Definition and 1000 Threads

Now this question really startled me. We all know that from simple energy conservation, the ball can reach a height of 2l, i.e reach the top point of the vertical circle if a speed of is given at the bottom ##\sqrt{4gl}## as mentioned in the question. Hence, I expected the answer to be A...

Hi, I have a project for my Dynamics and Vibrations class and I wanted to do it on the vibrations of a record player. Does anyone know what equations would be most relevant? I know this is a very general question but the project is large so I'm still figuring it out! Any thoughts are super...

Hi, I'm struggling to understand how two different coordinate systems come together. In this question, I reached my answer for the angular velocity which was incorrect. The correct answer is ω = 0 rad/s I think my biggest error happen in the step where I equated vB to each other. When I did...

This topic is not about the pinned pages, but I went to the dilation page on the FAQ and it seemed incomplete. https://www.physicsforums.com/threads/time-dilation-definition-what-is-time-dilation.763074/ A quick review since the page is locked "Time dilation is the factor by which an inertial...

My answer is ## \sqrt((300^2)+300^2)## = 424 after superimposing both ##cos13πt## and ##sin13πt##, After which, the overall of amplitude of superimposed of all 4 forces are ##\sqrt( (434^2)+ (500^2) + (600^2))## = 893, correct me if I am wrong

For g) how should I argue this claim? To me it seems straight forward because u is linearly related to z. Then so do their derivatives. And by the description of the model, ##\dot z## is linear to y. So it's quite obvious but not sure what I should pay more attention to when I write my proof...

I don't seem to understand the difference of accelerations when a cord is wrapped around cylinders and spheres. What I was taught is that if the cord is wrapped around a cylinder/sphere, the acceleration of the cord and whatever it is connected to will be twice the acceleration of the cylinder...

Hi, I'm currently looking to improve my understanding (mostly conceptually) on Dynamics (such as colllisions)and Statics of Bodies that aren't perfectly rigid, while considering mass, density, thickness, shape , kinetic energy, momentum and material stiffness/strength/toughness.

In my working, I have drawn a free body diagram of the LHS of the beam, I obtained some equations but after that not sure what I need to do. Usuaully in vibration problems you are given BC's then you plug them into the general solution to obtain the frequency equation. Please can you help me...

For the rod and the two particles ##x_1## is not zero but we have:$$x_2=x_3=0$$ We start with inertia tensor of the rod: $$ I_{ij} = \int \lambda ( \delta _{ij} \sum_{k} x^2_k -x_i x_j ) dx_1$$ $$ \lambda = constant = M/L $$ Using above equations, we have: $$I_{11} = \dfrac M L \int ( x^2_2...

I intuitively understand that it has 2 degrees of freedom (rolling without slipping - RWS), but I struggle to formalize this according to the rules of the art: I obtain: 10 - 3 (ground) - (rolling without slipping constraint) = 2 how to precisely calculate the RWS constraint? what formula and...

Let’s say we have a pulley with some box attached to it, mass of the box is ##m##. We consider rope to be massless and inextensible and pulley to have mass but be frictionless. How can tension apply torque on pulley?

This letter in PhysRevLett describes molecular dynamics simulations to investigate the underlying factors that drive osmosis. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.024501 Copy on Internet Archive ...

##\vec n_2## points to the diagonal top left. The velocity v is a function of t. So for example ##2t^2## and a = dv/dt. Putting the velocity vector into ##\vec n_1## and ##\vec n_2## terms. $$\vec v = v sin\theta \vec n_1 + v cos\theta \vec n_2$$ $$\vec v = -v \vec i$$ $$\vec a = \frac{d\vec...

I have been trying to solve this problem for hours using the mentioned equations but no matter what I do I cannot get the correct answer, that is v = 22.4 m/s. I thought that maybe if I could get an expression where v is a function of time I could solve the problem but I don't know how to do...

Hello, I understand the equation that describes the angular accelerator when 3 reference frames are involved is: Now I would like to ask what is the resulting equation when accounting more than 3 reference frames, i.e. when n-reference frames are involved. Thank you.

TL;DR Summary: Are the k and the w linked? Yesterday I came across this problem: A mass is attached to a spring and the system rotates (one of the spring end is fixed) in an horizontal plane. Given the mass m, the value of k, the length of the spring l_0 and the angular velocity w, compute...

The questions and relevant formulas/information are attached below: I started by writing the needed values: 2 kN = 2,000 N 6378 km =6378(1000) m 1800 km = 1800(1000)m After converting, I tried solving for the mass using the law of gravitation formula: I decided to replace N as...

HI! I tried to solve this exercise, by assuming that it is an inelastic collision, the planet is spherical, and that the rotation axis is parallel to the z-axis, see the figure attached. (1) before the collision, (2) after the collision.I started by assuming angular momentum conservation, which...

I am facing a problem while wanting ##\phi## dynamics in a cubic potential; ##g\phi^{3}##. The equation of motion I get for my case is(this follows from the usual Euler-Lagrange equations for ##\phi## in cosmology--Briefly discussed in Carol's Spacetime Geometry, inflation chapter)...

TL;DR Summary: How do I approach the setup of this problem? It seems very different than a setup for a kinematics problem I'm self studying first year mechanics and am having a hard time with the following problem (screenshot attached). The example is from Intro to Mechanics by K&K. I'm...

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...

I have tried to approach in the following way I am stuck. How should I approach this next.please help

Dear All, I tried to solve the attached question. it's about Couette flow, where the 2 plates move. in fact, I have to find the stability condition. is someone familiar with this and can help? many thanks, uria

Two point-like particles of mass m. The particles are rigidly connected to each other with a mass-less rod of length L. The particles are initially at rest in such a way that one particle is at the origin and the other is at the point (0, L). A point-like particle of mass M collides with a...

We know that in 1D, we can perform the following steps to obtain velocity in terms of time if the velocity is a function of position: $$v=f(x)$$ $$dt=\frac{dx}{v}$$ $$t_2-t_1=\int_{x_1}^{x_2}\frac{dx}{v}$$ $$x(t)\rightarrow v(t)$$ But I wonder if it is possible to obtain ##\vec v(t)## from...

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?

I got 13N but is that right because apparently, it's wrong Here's my work: F = mg = 2(10) = 20N F = ma a = F/m = 20/4+2 = 20/6 = 10/3 = 3.3m/s^2 T = mg - ma T = (2kg)(10m/s^2) - (2kg)(3.3m/s^2) = 13.4 N I appreciate it! And if I'm wrong could you show how you got your answer? Thanks

Because my little work project involves fluids I thought this the best topic to post under. I took the route of biological sciences and computer science. This area is out of my league at the moment I'm not sure the amount of time that would be required to get the material applicable to this...

I was modeling the dynamics of a vehicle for a project, and started doubting about the way of applying physics in this particular case. The thing is, I know the torque in the wheels from the torque the electric motor I designed do provide, multiplied by the gearbox ratio. I also know the...

Since no one seems to have mentioned this yet... For anyone interested in graduate-level study galactic dynamics, Jo Bovy (Assoc Prof in the Astrophysics Dept at U. Toronto) is in the process of constructing an interactive textbook on the subject, which you can check out at galaxiesbook.org...

I have run into a problem when trying to model a simplified vehicle that has three degrees of freedom – roll, vertical and lateral motions. It is represented by a single mass with two links that model the suspension behaviour. The links connect the tyre-to-ground contact points (tc) to the body...

I was having trouble with a physics problem (string tension dynamics) In this case I have a model that simulates the phalanges of a human finger. Each phalanx is a block of mass m1, m2 or m3 respectively. And to simplify it, consider the 3 equal masses. These phalanges are linked by joints that...

I have drawn three free body diagrams, one for each box and then I applied Newton's Second Law after choosing a reference frame rotated clockwise by ##\alpha##, with ##x## pointing south-east and ##y## pointing north-east and I got: ##\begin{cases}m_{1x}: -T+m_1g\sin(\alpha)+F_{fr_{12}}=m_1...

Trampolines are in effect coupled springs, with the mat being the much softer spring generally. E.g. On my Acon, when jumping about 1 meter, there is a max cone of depression about 60 cm deep and 1 meter across (1 meter point has a depression of only about 10 cm) At this same point the 160 or...

Developers of Shape Dynamics (as Julian Barbour and Tim Koslowski) claim that Shape Dynamics will offer in most cases the same predictions as GR, and implicitly as SR. How can this possibly be true, since they get rid of time altogether and thus of any notion of simultaneity? How would they get...

Shape Dynamics implements nicely Mach's principles. But how well does it fare when it comes to Quantum Mechanics? How can it be experimentally distinguished from other theories?

The figure illustrates the situation. The radii of the larger and smaller discs are 2R and R, respectively. Their masses are M and 2M, respectively (the largst disc has the smallest mass). Also, m=5/4 M, where m is the mass of the suspended object. The pulley is "massless" (negligible moment...

I'm stuck in a problem of a spring mass system with a pendulum attached to it as showed in the figure below: My goal is to find the movement equation for the mass, using Lagrangian dynamics. If the spring moves, the wire will move the same amount. Therefore, we can write the x and y position...

[Mentor Note -- thread moved from the technical forums to the schoolwork forums] I have a hollow-cylinder wheel model, braked with brake pads located at a distance d of the wheel's center axis. The brake pads have a contact area S. They are also forced towards the wheel with a pressure p. The...

I am trying to mathematically prove the Static Pressure Head equation: H = p/ρg How can I prove this equation and thus determine the nature of the relationship between these variables?

I'm not too sure how to account for both the mass and the rope at once. I think the following are true for the two individually: For the mass at the end, ## T = m ω^2 L ##, following from ##a = v^2/r##and ##v=ωr##. For the rope, ##dT = ω^2 r dM##, where ##dM = λ dr## and λ is the mass per unit...

I have found a fair amount of sources for studying polarized light but I haven't found sources discussing synthesis of polarizers in detail along with mechanistic discussion.

Hello, everyone! In the first few chapters of Physics 1, there is the description of motion, and the computation of the acceleration vector as being the sum of the rate of change of velocity, with the division of linear velocity squared by the instant radius of curvature: The above equation...

So I don't understand "due north from a position at colatitude ##\theta## " , whether how I translate it... I keep getting that direction should be radial...(toward Earth CM) This is my work: Thank you so much!

A) I am not sure if initial velocity means the initial velocity of the putty. If then, it should be 10m/s. But the answer given is 10/7 m/s B) i have solved this part correctly C) the answer should be 86J Please be kind to help me