Rotating Definition and 1000 Threads

A disk is dropped on a platform rotating at a constant angular speed ##\omega_i## as shown below. The question asks whether the final kinetic energy of the platform is conserved. I understand the angular momentum is always conserved provided that the net torque is 0, so I wrote the following...

This isn't really a proper homework question, but something I wondered about myself. To simplify things, we say that pivot point is in the origin of a Cartesian coordinate system, and the angles are constrained to the first quadrant. We see that the weight of the barbell is given as $$F =...

[No template as this thread was moved to the homework forums after it had attracted several replies] Here I have a tutorial problem as follows: The problem I have is about part a, whose answer is as follows: When I solve the partial derivative on Vf w.r.t. r, I get Vf = mω^2rsin^2(θ)/2...

"A smooth horizontal disc rotates with a constant angular velocity ω about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that point with velocity v0. Find the angular momentum M(t) of the disc relative to the point O in the...

There is no net external torque since the cylinder is slipping (no friction), so the angular momentum should be conserved. $$L_f=\frac 12MR^2\omega_i=\frac 12\times3.8\times0.52^2\times50\times\frac{2\pi\times0.52}{60}$$

In my textbook, the effective force of a particle on a rotating frame is given as below: The diagram is: What I do not understand is the expression for Rf dotdot, which is given as below: According to the book, an arbitary vector Q can be expressed as: So Rdotdot w.r.t fixed frame can be...

Denote ##v=(1,2,3)^T##, ##\theta=\arctan(2)##, and ##\phi=\arctan(\frac{3}{\sqrt{5}})##.The way that I attempted this was by performing the following steps: (1) Rotate ##v## about the z-axis ##-\theta## degrees, while keeping the z-coordinate constant. (2) Rotate ##v## about the y-axis...

I got the correct answer for the first part but I'm not sure why the answer for (b) is the same for (a). Wouldn't the rings falling off mean that I_f = \frac{1}{12}M_L L^2 only where I_F, M_L, L are the final moment of inertia, mass of the rod and length of the rod as opposed to I_f =...

If i put a rotating stick behind lens of several types, so the stick center is behind the lens center, will the stick edges always appear to move at the same rate as areas closer to the stick center?

Lets say we have a system of two point particles (1. and 2.) which are rotating around an axis. What is written next in my physics course book is: The torque of a 2.body on the 1. body is M21=r1xF21 and the torque of the 1.body on the 2.body is M12=r2xF12. Understandable. But how? There is no...

Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod. The blue line is a fixed column structure. CE and BD form the rotational...

I am looking for a rotation devise like that one in this video below (from 00:40 seconds). Does anyone know where to get one, or have any idea about how to create a nice and stable rotation setup for experiments without too much hassle and DIY? A bike wheel won't do, a disk is better, because I...

I have observed that when i throw a card and give it a angular velocity, it "aim" to vertical and depending on direction start to rotate. For example if it rotates to the left in horizontal, vertically left side of cart goes up and right goes down. Conversely for the right rotation. I am not...

Hello, i have a problem that look's easy to solve but really is not. It involves a rotating paddle wheel submerged in water and i want to know the force exerted on the wheels and the torque required to rotate it. I have made a simple drawing to illustrate the problem below. I want to use the...

I calculated the total moment of inertia of the system to be ##2ml²Sin²θ##, so the angular momentum is ##2ml²ωSin²θ##. To get the torque on the system I need to differentiate the angular momentum but I don't have any time dependent terms. What should I do?

I just came across a 2016 paper [1] that claims to have computed reasonably accurate masses for hadrons using what it calls a "rotating lepton model" and "the relativistic Newton equation". An earlier 2001 paper by two of the same authors [2] appears to be the first introduction of the general...

Summary:: This is a question about finding the acceleration of a point in a mechanism Hi, I have a question about the mechanism shown in the attached picture: Question: We are told that \omega = 6 rad/s and the first part is asking me to find the acceleration of point P on the piston when...

I would like to undertand more the force caused by unbalance in a rotor, assume that the bearing is represented with 2 springs like above: The geometrical center of the rotor ##O## is equivalent to it center of gravity ##C_g## and the center of the stator (bearing) ##O'## The rotor is perfectly...

I was thinking about a situation related to Galilean relativity but couldn't come up with a solution to the problem. I would be very grateful if someone can explain it to me. So, I was thinking of a situation where I am in the reference frame of a block moving at velocity u along the x-axis and...

Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...

I am struggling to get my work to match the posted solutions to this problem. I understand part (a) but can’t get the integral to work out for (b). I know I have to use Biot-Savart and add up the components from the the surface and volume currents. The cylinder is very long, so I need to make a...

Hey everyone! Was trying to answer this question and was wondering if this was the right way to go about it? Any help would be really appreciated!

Some information Newton's second law in a non-inertial frame is given by: Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) r', v' and a' are...

A rod rotates freely (edit: about an axis perpendicular to its length) in empty space. Working in an inertial coordinate system where the rod rotates around a fixed point, the rod is straight, of length ##2L## in its spinning state, and its mass distribution is symmetric along its length. The...

Firstly I deduced that in this situation the moment of inertia I, is not going to be parallel to w. And I calculated it as a matter of the angle, for the rod and the two point particles attached (with a mass 'm'), and the total moment of Inertia ended up being: I=((R²*sin²α)/2)*(M/6 + m) Being...

For a infinitesimal wire of lengh dx, the induced potential difference in an uniform B field perpendicular to it's motion is : dE=B.Vp.dx, where Vp is the component of the velocity perpendicular to the wire. Looking to the big wire I tried to take an arbitrary point express dE in function of...

Sorry if i made any language errors, English isn't my first language. Question: The limited area in the plane is created when the space between the line y=1 and the graph to the function f(x)=3*x/(x^2+1) rotates around the y-axis. Calculate the volume of the solid.I want to sum up all the...

To start off with, I can't seem to interpret the FBD here. Here are my drawing: and what I interpret as. From here, I feel like I can (it's wrong obviously but I'm not sure why) state that sin theta = o/h = o/mg = N/mg , so N= mg sin theta? Thanks

Is there a way to calculate the average linear speed of all points in the volume of a sphere rotating on a single axis? Since points closer to the axis of rotation and the poles move slower than points further out, would the average speed be a simple function of r/2 and pi? It would seem that...

The increase in radius is due to the centripetal force acting on the ring. The centripetal force acting on each point of the ring is directed towards its center. We can find force using ## F_c = M(\omega)^2R## We can use this ##F_c## in the equation of Hooke's Law to find the elongation Could...

If a rod is on a table (horizontally) and rotating about an axis that passes through one of its ends and vertical to the table, what would be the tension on the opposite end of the rod (the end opposite to the axis) . In this post (Check this post out from Socratic QnA), the limits take while...

Homework Statement: Solve parametrically the system with g, load cell measurements and know accelerations. Homework Equations: to be found Consider that we know angles tetha(t) of a mass-less link rotating about its centerr O. - so we also have velocities and accelerations - and values of...

Let ##(r,\phi, \theta)## be the radial, polar and azimuthal coordinates respectively. As ##\vec{B}## is confined to ##xz## plane such that ##\theta = \alpha## I assumed ##\vec{B}## on the surface of shell to be ##\vec{B} = a\sin(\alpha) \hat x + \cos(\alpha) \hat z \tag{1}## Surface area...

a) Our force can be represented as: $$\vec F= -k(r-H) \hat r$$ then the equations of motion are: $$\hat r: \ddot r -r {\dot{\theta}}^2=-\frac{k}{m_1}(r-H)$$ $$\hat{\theta}: r \ddot{\theta} + 2 \dot r \dot{\theta}=0$$ Plus we know that angular momentum is constant then $$|\vec L|=m r^2...

Hello, I know it suppose to be a relatively basic question but still somehow I can't fully understand it. Let assume that a man jumps vertically on the equator, while the Earth is of course rotating. What will happen to the value of his linear momentum in the horizontal axis? It seems to me...

Say I have a motor connected to a wheel, the wheel is driven forward. The motor produces a certain torque rotate/turn the wheel right or left, how do I calculate the torque needed to rotate? keep in mind the friction between the surfaces, the mass of the wheel and the tire sag/subsidence due to...

Can someone check if my answer is correct please? Question: If liquid contained within a finite closed circular cylinder rotates about the axis k of the cylinder prove that the equation of continuity and boundary conditions are satisfied by u = ΩxR where Ω = Ωk is the constant angular velocity...

As I`` m learning for an upcoming exam I found an electrodynamics problem I struggle with. In the first task I need to calculate the magnetic dipole moment of a uniformly charged,thin disk with the Radius R and a total charge Q which rotates with a angular speed omega round its symmetry axis...

Sorry if this is a stupid question but I couldn't find an answer anywhere. According to 2 scientific papers, the neutron star PSR J1748-2446ad has a rotation rate of 716Hz, which equates to a linear surface speed of 0.24c. What if this star was originally rotating, let's say, 5 times (or more)...

(The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite). I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...

A) The slider experiments three forces, all of them are on the ##x## axis (considering ##x## axis as the axis aligned with the arm): Normal force (exerted by the support), elastic force and centrifugal force, which is ##m.(\omega^2 r)## Elastic force is equal to ##Fe=-k \delta =-2 (R-2R)=2R##...

The sketch above shows the situation of the problem. Clearly, as the rotation is taking place in the ##y-z## plane, the x-components of the two vectors remain unchanged : ##A_x = B_x##. Let the projection of the vector ##\vec B## on to the y-z plane be vector ##(\vec B)_{yz} = B_y \hat y + B_z...

Firstly, I need to determine what the electric field is causing. Using left hand rule, the force due to the field is acting down the slope. Hence my FBD looks like: Where the two arrows pointing towards the right represent the force due to the field and weight of the cylinder. Since ...

Its velocity, Vp, is towards some other part of the universe, It rotates in the same plane as its direction of travel. The linear velocity of an object on the surface of the planet relative to the centre is Vr. That means the object's total linear velocity is Vp+Vr when it's at one point in its...

Summary: Will the motion around us become faster when we travel faster? When we approach a body rotating on its axis with certain speed v, will we see the body rotating in speed slightly more than the v during our motion ?And what happens assuming that we are approaching the same body in speed...

Well, I tried plugging the data in the formula. I know that ##\vec a_b = 0; \vec \omega=3 rad/s ; \vec r## can be calculated using trigonometry. Then I also know that ##v_{relx}= 10 cm/s##, ##a_{relx}=15 cm/s^2##, ##\vec {\dot{\omega}}=-10 rad/s^2##. But how do I get ##v_{rely}## and...

Problem statement: Two rings rotate with equal and opposite angular (relativistic) velocity about a common center. Matt rides on one ring and Eve on the other and there's a moment they meet and their clocks agree. At the moment they pass by one another, each asserts that is the other's clock...

The red arrows correspond to the areas the solenoid will be moved too

The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot...

Let $R$ be the region $\left\{(x, y) : 0 \leq x \leq 1, 3^x − x − 1 \leq y \leq x\right\}$. Find the volume of the solid obtained by rotating $R$ around the line $y = x$.