Motion Definition and 999 Threads

I'm in trouble trying to understand the expression ##t= \frac{1}{\omega} cos^{-1}(x/A)## that comes from ##x = Acos(\omega t)##, in which ##A## is the amplitude, ##t## is time and ##x## is displacement. When ##x = 0##, ##t = \frac{\pi}{2\omega} ##, shouldn't it be 0 since there was no movement?

Homework Statement A) By examining the effective potential energy find the radius at which a planet with angular momentum L can orbit the sun in a circular orbit with fixed r (I have done this already) B) Show that the orbit is stable in the sense that a small radial nudge will cause only...

<< Mentor Note -- thread moved from the technical forums, so no Template is shown >> Show, from the first principles, that the equation of motion of a mass (m) on a spring, subjected to a linear resistance force R, a restoring force S, and a driving force G(t) is given by d2x/dt2+ 2K(dx/dt) +...

Homework Statement Homework Equations F = ma The Attempt at a Solution I couldn't draw the freebody diagram. There's this weight of mass m, which is mg, downwards from m and there's tension T to upwards. This T affects mass M in the +x direction, but how could i find out the normal force...

Homework Statement A particle is projected inside a tunnel which is 2 m high and must not hit the side or ceiling of the tunnel. If the initial speed is U show that the maximum range of the particle inside the tunnel You may assume that the maximum range is attained when the projectile just...

It has often been posed that one reason humans cannot feel the motion of the Earth as it spins and moves around the Sun is that our bodies have acclimated to this motion due the fact that it is all we have ever known. If true, does this mean that astronauts have experienced feeling the motion...

The Faraday paradox is a very curious example in the topic of relative motion. An experiment demonstrating the curious results is shown in the video below: This has made me curious about the linear version of the Faraday paradox. A conductor placed atop a magnet, both at rest in one scenario...

Homework Statement While solving equation of rocket motion with Newton's law in 1-d,I pondered to apply Lagrangian method on this. However, I didn't get correct result. Because I can eliminate last 2nd equation using last equation and get some other equation which is certainly not rockets...

First time poster here, thanks in advance! I have a project I'm working on, and I'm looking for a way to limit the rotational motion of a shaft inside a cylinder. The cylinder is fixed, and the shaft is spinning inside the cylinder coaxially. Basically, torque will be applied to the shaft...

Homework Statement Question: A 600 g steel block rotates on a steel table while attached to a 1.20 m-long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 5.01 N perpendicular to the tube. The maximum tension the tube...

IMPORTANT! TEXT IN GREEN HAS BEEN ADDED AND IS CORRECT TEXT IN RED HAS BEEN REMOVED AND IS INCORRECT 1. Homework Statement Question: An energetic father stands at the summit of a conical hill as he spins his 25 kg child around on a 5.7 kg cart with a 2.3-m-long rope. The sides of the hill are...

I attached an image with problem and the associated illustration. I don't know what the relevant equations are for this problem. Each and every time I read the problem I keep drawing a right triangle to represent the velocity components. The problem says the river is flowing east at 5km/h. I...

Homework Statement First problem: The speedometer in a car is driven by a cable connected to the shaft that turns the car's wheels. Will speedometer readings be more or less than actual speed when the car's whells are replaced with smaller ones? Second problem: Keeping in mind the concpet from...

Homework Statement A particle A moves along a circle of radius ##R = 50 cm## so that its radius vector ##r## relative to the point O (Fig. 1.5) rotates with the constant angular velocity ω = 0.40 . Find the modulus of the velocity of the particle, and the modulus and direction of its total...

https://i.imgur.com/4nynNBg.png I cannot understand for the life of me why this problem doesn't just use T = 2πr/v to solve for the period to get T = 2π(Lsinβ)/v. Instead, it rearranges the formula for a(rad) = (4π^2R)/T^2 to solve for T, and arrives at a totally different answer, T =...

Homework Statement determine the acute angle (in radians) of appropriate elevation in the throwing of a ball, if the initial velocity is 20 m / s, g=9.81 m/s^2 and the distance in x is 40m. The ball leaves the hand of the pitcher with an elevation equal to 1.8m and the catcher receives it at...

Homework Statement Two particles A and B of masses m and 2m are attached to the ends of light inextensible string which passes over smooth fixed pulley. The particles are released from rest and when particle B has moved h meters, it hits the ground and does not rebound. (i) Find the speed of...

Homework Statement I'd like to derive the equations of motion for a system with Lagrange density $$\mathcal{L}= \frac{1}{2}\partial_\mu\phi\partial^\mu\phi,$$ for ##\phi:\mathcal{M}\to \mathbb{R}## a real scalar field. Homework Equations $$\frac{\partial...

Homework Statement Homework EquationsThe Attempt at a Solution I need help in solving second part of this question. I put ## e^{i \alpha }\psi ## instead of ##\psi ## and got to see that the integrand doesn't change which means the given transformation is a symmetry of the given action. But...

Homework Statement I am solving a kinematic problem, where I have a link that is attached to a rotational joint. I need to find the position of the joint for t=0..8, and I need to do it for every 0.01s. The problem comes from the fact that I have three stages for the velocity, during t = 0..0.1...

[Mentors' note: This thread was split off from another thread about the cosmic ray muon measurements] The particle at rest in the moving ship is moving against the Earth. The particle at rest on the Earth is moving against the moving ship. A scientist in the moving ship measures the life time...

Homework Statement A baseball is hit into the air, nearly vertically, with a speed of 27 m/s. When it comes down, the ballplayer catches it in his glove. Air resistance (drag) is actually fairly important for a baseball in flight, but for now let’s assume it is negligible. (a) How high does...

Homework Statement equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given. the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot...

Ive been lying in bed this morning wondering about the unusual motion of stars in galaxies.The whole disc rotating like a record at the same speed.Does it mean that the effects of gravity are simply altered by speed?Much like a wonder-wall.So the faster the speed of the object,or stars,the less...

Homework Statement A frog jumps at t=0s and follows a projectile motion. The maximum height he reaches is 0.45m. The air resistance can be neglected. a) What is the initial speed of the frog in y-direction and how long is the total time until he lands on the ground? b) At which degree should...

So I was in the bus going to school. I sat in the back not directly underneath the emergency exit but more like behind it. Anyways, since it’s been raining consistently, the emergency exits sometimes leak. So I’m sitting down and my jacket sleeve gets wet with a drop from the emergency exit. I...

Hello everyone, I am new here, and wondering if anyone would have some knowledge on a current problem I have been working on. I am trying to create time- and frequency domain 3D models of an object hanging using a spring from a fixed point within a shell. I am trying to figure out how the...

Hello, For 2D motion, I understand that velocity, position and acceleration of a point object can be described using the fixed basis vector ##\hat {i}## and ##\hat {j}## and the rectangular coordinates ##x(t)## and ##y(t)## which which are functions of time ##t##. Another option is to use...

Homework Statement Calculate the harmonic motion equation for the following case A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2 Homework Equations x(t)= +/-Acos/sin ( (2pi/T)/*t) The Attempt at a Solution [/B] A is given to be 0.1 so I simply place it into the equation. Now I have to...

Homework Statement The problem is taken from Morin's book on classical mechanics. I found out Lagrangian of motion. Now to solve, we need small angle and small x approximation. The small angle approximation is easy to treat. But how to solve small x approximation i.e how do I apply it...

Q)6.10 in Morin's Classical Mechanic. All that I have to do is find Lagrangian here. After that only simple motion. Finding Lagrangian: Choose the coordinate system at the centre of hoop as shown in 2nd attachment. Then,I found out Lagrangian of the system. Invoking E-L Equations to find the...

For projectile motion problems, we say that the horizontal component of the ball's path has no acceleration. The vertical component does, which is due to gravity, but in projectile motion it is true that horizontal and vertical motion are independent of each other. My question is in regards to...

Homework Statement You throw a ball straight upward with initial speed ##v_0##. How long does it take to return to your hand? Homework Equations ##v=v_0+at## ##x-x_0=v_0t+\frac{1}{2}at^2## The Attempt at a Solution My question is a general one that relates to the described solution. According...

Homework Statement A particle of mass M, with charge Q is left at the point A. After reaching point P the particle is at the effect of a constant and uniform magnetic field of intensity B reaching point Q. Find H. Homework Equations P=mg Fm=qvB Ke=(mv^2)/2 U=mgH The Attempt at a Solution...

Homework Statement How would you describe the motion of a string at two adjacent antinodes? Homework Equations N/A The Attempt at a Solution So would the antinodes not be moving since it's a standing wave? Or would they be moving in phase because they are propagating together?

Hi There is an example in my textbook worded as follows; A particle of mass 2kg moves along the positive x-axis under the action of a force directed towards the origin. At time t seconds, the displacement of P from O is x metres and P is moving away from O with a speed of v ms^-1. The force has...

Hello everyone, A rigid body is a system whose points, pairwise, always keep a constant mutual distance. Let's say the body is in a certain configuration ##C_0## at time ##t_0## (which means that each point has a specific velocity and position relative to a fixed lab reference frame) and the...

Homework Statement Making a turn, a jetliner flies 2.1 km on a circular path of radius 3.3 km. Through what angle does it turn? Express in 2 significant figures. Homework Equations Arc length = ##S=rθ## The Attempt at a Solution Please see the attached image. I've tried multiple different...

Homework Statement A car and motorcycle are racing along a runway. The motorcycle first takes the lead because it's constant acceleration ##a_m=8.40~\left(\frac{m}{s}\right)^2## is greater than the car's constant acceleration ##a_c=5.60~\left(\frac{m}{s}\right)^2##. But it soon loses to the car...

I would like to preface this by saying that I solved the homework problem, but my professor gave me an added challenge of finding the period of the motion described in this problem. 1. Homework Statement The pendulum bob of mass m shown in the figure below is suspended by an in-extensible...

If expansion is moving objects away from each other in space, does that imply an interface of some sort between space and mass, a connection, or friction? If so, how is it that mass can drift through space and not eventually come to a stop? If moving space exerts a force on mass, why wouldn't...

Homework Statement The evolution of the density in a system of attractive spheres can be described by the following dynamic equation. $$\frac{\partial}{\partial t} \rho (r,t) = D_o [\nabla^2 \rho (r,t) + \beta \nabla \rho (r,t) \int dr' [\nabla V (|r-r'|)] \rho (r',t) g(r,r',t)]$$ a)...

Salutations, I have been trying to approach a case about projectile motion considering variation of gravity acceleration and air resistance: A spherical baseball with mass "m" is hit with inclination angle $\theta$ and launching velocity $v_0$, then, the wind has a drag force equals to ##F=kv##...

A block of mass 3.00kg is pushed up against a wall by a force of P that makes a 50.0 degree angle with the horizontal (REFER TO PICTURE). The coefficient of static friction between the block and the wall is 0.250. Determine the possible values for the magnitude of P that allow the block to...

Homework Statement A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle θ as shown in the figure below. (a) Derive expressions for the initial accelerations of the...

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...

Is there any thing like perceived gravity in circular motion?? If I consider that it is in opposite direction to centripetal force, then both perceived gravity and centripetal should cancel each other and object should move in a straight line. Why does it nit happen?

Homework Statement A car is moving up a rough inclined plane/road of 10 degrees with a velocity of 10m/s. The coefficient of friction is equal to 0.5 and the mass of the car is 10kg. The car brakes. After what distance does the car stop? Homework Equations F=ma v^2=u^2+2as u= initial velocity...

Homework Statement "The slingshot exerts 40 N for 0.25 s. If Red bird is released 5 meters above the ground, and kills the pig, how far away is the pig?" m = 0.75 kg; angle = 45 degrees Homework Equations x = (initial velocity in x-direction) * (time)[/B]The Attempt at a Solution In order to...

Recently I was playing around with the idea of graphs of projectile motion and I started wondering what it would look like if someone were to graph every parabolic trajectory of a single initial velocity over all angles between o and 90 degrees above the horizontal. I decided to find out so in...