Rotating Definition and 1000 Threads

Homework Statement A disk rotates with constant angular velocity \omega. Two masses, m_A and m_B, slide without friction in a groove passing through the centre of the disk. They are connected by a light string of length l, and are initially held in position by a catch, with mass m_a at a...

A load of mass 250kg is required to be lifted by a means of a winding drum and cable. The mass will be initially at rest, accelerated uniformly upwards for 4 seconds and then decelerated uniformly for one second. such that a final height of 10.5 metres is gained. The winding drum has a mass...

Homework Statement A mouse starts running on a circular path of Radius = 28m with constant speed u = 4m/s. A cat starts from the center of the path to catch the mouse. The cat always remains on the radius connecting the center of the circle and the mouse and it maintains magnitude of its...

Homework Statement Hello everyone, How do I go about this problem; Describe the motion of the particle, m, inside the rotating tube. (See attachment please.) At time t=0, r(t=0)=b and \dot{r}(t=0)=v_{0} Homework Equations I think it would be practical to use polar coordinates to describe...

Homework Statement A metallic chain with a length ‘l’ andd whose ends are joined together is fitted onto a wooden disc as shown in the figure.The disc rotates with a speed of n revolutions per second.Find the tension of the chain T if its mass is m. Homework Equations The Attempt at a...

Homework Statement Hi everyone! I'm struggling to understand how to solve this problem, I searched on the web, but I didn't find anything similar. I have a motor delivering a power P=5kW at n=1500rpm. This motor is mounted on 4 supports, each having a rigidity k=15kN/m. I know that distance...

I am referring to "Newton's bucket" -- essentially a hollow cylinder filled with water inside which rotates about the cylinder's axis. The result is that the surface of the water is a parabola. The argument for this is that the surface normal of the water must be directly opposing the other...

I am sure this is not the best description of the problem, so let me know how I can clarify. Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames. What's known is 1) A...

Homework Statement I have attached the problem as a picture on this post, am really really unsure on how to start! so far the only thing i can think of doing is using this equation (\frac{d^{2}r}{dt^{2}})_{s} = ( \frac{d^{2}r}{dt^{2}})_{s'} + 2ω \times (\frac{dr}{dt})_{s'} + \dot{ω}...

Hi Everyone, Suppose that we have cylindrical coordinates on flat spacetime (in units where c=1): ##ds^2 = -dt^2 + dr^2 + r^2 d\theta^2 + dz^2## I would like to explicitly calculate the expansion tensor for a disk of constant radius R<1 and non-constant angular velocity ##\omega(t)<1##. I...

Homework Statement The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...

I was solving this paper, but got stuck on this question, and it's been bugging me endlessly. I don't know what I'm missing. Here's the question: A rod of 20 dia is fixed to the ceiling of a roof on one end. A rotor of 50 kg mass is attached to the free end with bearings. The CG of the rotor...

Homework Statement for this question, since area of cutting of magnetic field change, so magnetic flux change, f is unchanged . but i don't understand why the torque will change since the force is unchanged, since torque=FORCE X DISTANCE FROM THE ROTATING PIVOT Homework Equations...

I'm reading Lanczos: 'The variational Principles of Mechanics'. I need help resolving a paradox - which is probably trivial… Lanczos (page 100 Dover edition) introduces a system, S', rotating at angular velocity \vec \Omega about an axis through a fixed point with respect to inertial system...

This problem is from Boas Mathermatical Methods 3ed. Section 16, problem 1. Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let z = ae^iωt be the...

Suppose that a wheel is rotating around its axis in free space with no friction, with no external forces acting on it. In theory, the wheel will rotate forever with constant angular velocity. This velocity is assumed to be small (essentially non-relativistic). Now, consider an observer O...

Homework Statement A thin copper (resistivity 1.7 x 10-8 Ωm, density 8.9 g/cm3) ring rotates about an axis perpendicular to a uniform magnetic field B0. Its initial frequency of rotation is ω0. Calculate the time it takes the frequency to decrease to 1/e of its initial value, under the...

Homework Statement a disk of radius 40 cm is rotating about an axis through its centre. the moment the inertia of the disk is 0.015 kg m^2 and it is turning at 3 rev/s. sand falls on the disk at a distance of 20 cm from the axis and builds a 20 cm radius sand ring on the disc. How much sand...

Homework Statement I have to find current absolute acceleration in attached picture in points 1,2,3,4 and draw vectors. The picture is rotating pendulum. The rest data show attached picture: Homework Equations [SIZE="6"]a[SIZE="3"]abs = [SIZE="6"]a[SIZE="3"]rel + [SIZE="6"]a[SIZE="3"]u +...

Homework Statement Introduction to Classical Mechanics by David Morin - problem 9.43, page 424 A uniform flat rectangular sheet of mass m and side lengths a and b rotates with angular speed w around a diagonal. What torque is required? Given a fixed area A, what should the rectangle look...

Suppose you have a body floating in a rotating superfluid. Maybe a speck of dust. Would it rotate? What if you have two bodies connected in some way. Would this system rotate around its center of mass?

Homework Statement A uniform disk of mass 2M, radius R, is mounted on a frictionless horizontal pivot through its principal axis. The disk has an additional point-mass, M, fixed to a point on its circumference. (a) Give the Lagrangian for this system. (b) Find the frequency of small...

Homework Statement A body with mass ##m## can move without any friction on ellipse that ##(x/a)^2+(y/b)^2=1## describe. In ##y## direction homogeneous gravity field ##g## is present. For generalized coordinate we take angle ##\alpha ## defined with ##x=acos\alpha ##, ##y=bsin\alpha ##. Find...

Homework Statement Around vertical axis ##O## a body on picture below (see attachment) is being rotated with constant angular velocity ##\Omega ##. On the circle we have a body with mass ##m##, that can feels no friction. Find position of that body as function of ##\phi ## and time. Calculate...

Homework Statement I'll provide picture for clearer understanding. The solid cylinder of mass ##m## and radius ##r## revolves about its geometric axis at an angular rate ##p## rad/s. Simultaneously, the bracket and shaft revolve about x-axis at the rate ##\omega## rad/s. Determine the angular...

Homework Statement So let's say I have a particle moving at some given latitude λ on or near the Earth's surface, northen hemisphere (see diagram attached). Look at the coordiate system I have x',y'and z' with origin on the surface...and the velocity I'm given has components along those primed...

Homework Statement I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, that's all I need help with. Progress Since the rod is...

Hello, I have a project whereby I am designing a toy that spins a horizontally positioned propeller, then releases it. After releasing it, the propeller gains height, but moves somewhat away from the operator of the toy. Is the direction of airflow through the propeller vertically? If...

Question on Acceleration of Rotating Objects: The Physics Textbook I have says that the Acceleration of a spinning object is the Pythagorean-theorum result of sides for Centripetal-Acceleration (toward the rotation center) and Tangential-Acceleration (perpendicular to Centripetal-Acceleration...

Homework Statement Hi, everyone. Me again. This time I'm here to ask about the tension in the string on a massive pulley. We have a wheel of radius R with a moment of inertia about its principal axis of 2/3 MR2 , suspended above the ground on frictionless bearings. A massless string of...

Homework Statement Consider a non conducting ring of radius r and mass m which has a total charge q distributed uniformly on it.The ring is rotated about its axis with an angular speed ω. a)Find the equivalent electric current in the circuit. b)Find the magnetic moment μ of the ring...

Homework Statement A horizontal 845.0 N merry-go-round with a radius of 4.3 m is started from rest by a constant horizontal force of 74.0 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 2.2 s. Assume it is a solid cylinder. The...

Homework Statement A copper wire loop is initially at rest in a uniform magnetic field (full flux going through it). Between times t=t1 and t=t1+(delta)t the loop is rotated about a vertical axis as shown (no flux going through it). Will current flow through the wire of the loop during this...

Homework Statement A massless spring of length b and spring constant k connects two particles of masses m_1 and m_2 . The system rests on a smooth table and may oscillate and rotate. a) Determine the Lagrange's equations of motion. b) What are the generalized momenta associated with...

Homework Statement I am basically designing a rotary drum dryer and need to know the positions of the bearings for the dryer to be stable. The drum is of length 17 m with diameter 3.24 m, inclined at 2° rotating at 3.24 rpm. I need to find the distance X and OY. (Given that Y passes through...

Homework Statement A 75g mass sits 75cm from the center of a rotating platform undergoing a uniform angular acceleration of 0.125rad/s . The coefficient of static friction between the mass and the platform is 0.250. What is the speed of the mass when is slides off? A. 0.889 m/s B. 1.26...

As I've red, different points on the rotating disk, or rotating object have different velocities and so they should time dilate differently. Points on equator are for instance quicker than those in Scandinavia. When we take an inertial frame that has zero velocity with respect to the Earth as a...

Homework Statement Two coordinate systems xyz (…fixed) and x0y0z0 (moving) coincide at time t = 0. The moving system is rotating about the …fixed z axis, which coincides with z0 axis. The angular velocity is given by ω = tk = tk0. The position vector as measured in the rotational frame is...

Homework Statement A homogenous, thin stick with the mass m and the length l is hanging from the ceiling and can rotate freely around the point P. A small ball with the mass of M is attached to the end of the stick. The small ball on the end of the stick gets hit by another small ball with...

Homework Statement Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis. Use cylindrical polar coordinates and let the equation of the parabola be z = kp2. Write down the...

I wish to synchronize a thermal camera FLIR A300/600 with a test section on a rotating shaft such that whenever the section becomes orthogonal to the line of sight of the camera, an image is clicked by it automatically. The camera uses a TTL pulse input. Being a mechanical engineer, I have...

2013 edits to the sci.physics.faq "Rotating Rigid Disk in Relativity" I was just reading the sci.physics.faq http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html on the rotating disk. I was really dissapointed by the recent (2013) editorial comments. I felt that they totally...

Hello To demonstrate that we can deduce from special relativity the existence of an observer who finds that his three-dimensional space is not euclidean (a conclusion that is false in my opinion), in subsection "Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference" of his...

Homework Statement Is it possible to determine the relative location of two points on a rotating rim by sending a signal that goes from one to the other, reflects, and then returns to the sender? Assume a rim, like a bicycle wheel rim without the tire or spokes; the interior surface of the...

Imagine a cylindrical space settlement. It spins about an axis to create pseudo gravity for residents, who will think that radially outward is "downward". The shape of this settlement is a toroid with a rectangular cross section. Air is pumped into make a habitable environment. Then...

I was reading a little about the behavior of non-inertial frames in relativity, since I'm interested in knowing how can we measure time on Earth and the sequence of events here. So as we know Earth is rotating and therefore the clocks on surface that are mutually at rest get desynchronized. Can...

Hi, I would like to clear some doubts over the field of a rotating magnet. I understand that in a typical alternator or generator , brushed or brushless , the current in the wires is induced because the opposite poles of either a permanent or electromagnet pass by the coils and the magnetic...

Homework Statement At t=0 a police officer is located at (0,R) on a circular platform whose radius is R and which rotates around the z axis with constant angular velocity ω. The officer's velocity at that point in time is (ωR ,0). At that time, a bird leaves the center of the platform along the...

This is NOT a HW question. I'd appreciate an explanation of the following: I would like to determine the forces acting on a mass set between two springs of constant k on a slope (the slope's angle is alpha). The slope revolves around the vertical axis with angular velocity w and the mass could...

Hello, I am looking for some direction to books or papers which may help me, When you solve the Helmholtz equation you end up with vector spherical harmonics as solutions. The Helmholtz equation is invarient under rotations which means that rotations of these solutions are also solutions...