Motion Definition and 999 Threads

Hi I have come across something confusing in rolling motion. If an object moves with a positive V_cm meaning to the right its angular velocity will be clockwise or negative. The formula is V_cm=wR but for a positive V_cm you get a negative w as it moves clockwise if V_cm is to the right...

$$i \gamma^{\mu} \partial_{\mu} \psi = m \psi_c \\ i \gamma^{\mu} \partial_{\mu} \psi_c = m \psi $$ Where ##\psi_c = C \gamma^0 \psi^*## Show that the above equations can be obtained from the followong lagrangian $$ L = \overline{\psi} i \gamma^{\mu} \partial_{\mu} \psi - \frac{1}{2} m \left...

I was reading about the Tusi couple and read it "as a solution for the latitudinal motion of the inferior planets, and later used extensively as a substitute for the equant". Since the Tusi couple is related to plotting out an ellipse, did Nasir al-Din al-Tusi already discover the laws for...

I believe I've solved this problem, however, I got through it pretty quickly and since it's the last problem on the assignment, I feel that I may have had an oversight. For part a, I got: fs=md(α^2)(t^2) and for part b, I got: ω=Sqrt((µs*g)/d) Could someone confirm my answers? I've attached a...

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For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...

In his thought experiment on the relativity of simultaneity, Einstein synchronizes two clocks A and B (at either end of a rod) to the clock C in a stationary frame, while A and B (the rod) is moving relative to C. The equations Einstein finishes with demonstrate how observers moving with A and...

I can't find the answer anywhere here's my question. can a centrifuge exist outside a field of gravity. More specifically, in a theoretical void of nothing without stars in view or any point of reference for comparison how could motion like spinning or acceleration exist?

Is it possible, that one physics law is "Everything is in motion?" (since zero doesnt belong to nature)...if so, does that implies that black holes move?

A recurring question is: while the motion of a polar Foucault pendulum is fairly straightforward, the case of a non-polar Foucault pendulum is quite difficult to visualize. In 2020, on physics stackexchange someone submitted that question and I contributed an answer. In a comment to another...

I'll risk a quick off-topic answer here, since I think it's straightforward QM, not vague "interpretation" stuff. :oldbiggrin: In QM (e.g., Ballentine p81), for a free particle, ##H = \frac12 \, M\, V\cdot V + E_0##. So in the ground state ##|E_0\rangle## we have ##H|E_0\rangle = E_0...

TL;DR Summary: Prove that a sum of trigonometric ratios is periodic but not not simple harmonic. We need to prove that ##x = sin{\omega t} + sin{2\omega t} + sin{4\omega t}## where ##x## is the displacement from the equilibrium position at time ##t##. I can see that each term is a SHM, but...

The block starts to slide if friction can no longer hold the block. F=u*n and F=(m1+m2)a so: (m1+m2)a=uN=>am1+am2=uN=>am2=(uN)/(am1) So:am2=(uN)/(am1) is the force. The answer is F=(u*m1g(m1+m2))/m2 I do not see how the acceleration terms are canceled. Is my answer equivalent to this?

For (c), Solution is Can someone please explain how they calculated that angle? I thought they would do ##arc\tan (\frac {32}{3.35})## Many thanks!

TL;DR Summary: Using vector functions how can I find the minimum average velocity (something greater than 11.86m/s) of a ball if the launch angle is unknown and if I have a point that the object must travel through (11.86, 3.47)? In my assignment, I developed a function for a lob shot...

I couldn't draw the motion after the collision, since the whole angular displacement of the plane got me confused.

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...

Can you explain with example what mean rotation is absolute and linear motion is relative?

(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...

I am stuck at A, how do you calculate the motion of the air? I know ρ=m/V but what is the mass of the air, or I got that question wrong? Thanks

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 how to even start the question

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...

T= m*vmax^2/r 1500 = (80kg)vmax^2/4.5

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.

Found the speed at which the masses will travel after their collision: 2.25m/s Not sure what to do next...

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...

How to find frictional force when coefficient of friction is not given?

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...