Rotation Definition and 1000 Threads

Homework Statement What is the moment of inertia of a spinning object of radius 0.5 m and mass 6 kg moving at 5 m/s, if it has a kinetic energy of 100 J? 1) 1 kgm22) 2 kgm23) 4 kgm24) 8 kgm25) 20 kgm2 Homework Equations K.E. = Kinetic energy of rotation + kinetic energy of...

Hi guys, I was wondering if it is possible to have a pure planar rotation of a rectangular-prism shaped rigid body on a planar surface when it is subjected to a planar point force at the tip. Is there any range for the point force such that it can not break the static friction force (so no...

Is it possible to replicate the Faraday rotation experiment for a high school junior? I am in honors physics (IB) and have been taught about waves, electromagnetism, energy transfers, etc. My physics teacher will guide me if I choose to do this. Is the experiment too ambitious?

Given A(2√3,1) in R^2 , rotate OA by 30° in clockwise direction and stretch the resulting vector by a factor of 6 to OB. Determine the coordinates of B in surd form using complex number technique. i try to rewrite in Euler's form and I found the modulus was √13 but the argument could not be...

I was reading the wikipedia entry for Dark matter halo here: https://en.wikipedia.org/wiki/Dark_matter_halo And they have this graph for the Milky Way galaxy rotation curve: "Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the galactic center. Horizontal...

Homework Statement I am doing a report or physics homework where I have to talk about the rotation of an Olympic high diver and am slightly confused as to how it all works. I have a few questions which would help clarify. 1) So I know that in the air, angular momentum is conserved as in the...

Homework Statement If a bike wheel rotates 9.4 times while slowing down to a stop from an initial angular velocity of 8.1 rad/s, what is the magnitude of the angular acceleration in rad/s/s Homework Equations α = at / r α = ω / t α = Θ / t^2 ω = Θ / t ω = v / r Θ = ω t + 0.5 α t^2 v final = v...

This isn't about a specific physics problem, but rather a question: Given I have a ball or cylinder rolling smoothly along some path, is it generally true that mechanical energy is conserved? I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##? I have been able to...

Homework Statement In the figure, a wheel of radius 0.42 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.7 kg box that slides on a frictionless surface inclined at angle θ = 28 owith the horizontal. The box accelerates down the...

Homework Statement A car is traveling at 27.8 m/s, it undergoes a negative acceleration of 2.6 m/s/s when the brakes are applied. How many revolutions will the tires go through before the car comes to a stop if the wheels each have a radius of 1.0 m? Homework Equations α = at / r...

What is an example of a rigid body rotating when one point is fixed and there are no net applied torques? And the fixed point is not the center of mass. I considered a cone rolling without slipping on a flat plane is such an example; the apex is the fixed point, but is there a net applied...

For the rotation of a rigid body about a fixed axis z the following holds. $$\vec{\tau_z}=\frac{d\vec{L_z}}{dt}= I_z \vec{\alpha} \tag{1}$$ Where \vec{\tau_z} is the component parallel to the axis z of a torque \vec{\tau} exerted in the body; \vec{L_z} is the component parallel to the rotation...

I want to rotate an inclined plane to achieve a flat surface. I think I can use the Euler angles to perform this operation. Using following data: and following rotation matrix I think you can make the plane flat by following rotations: 1: rotation around x-axis by 45° 2: rotation around...

Homework Statement A sphere (of radius r and mass m) rotating with angular velocity ω0 is lowered onto the edge of a floating platform of length L and mass M. The platform can move freely on water. The platform is rough and the sphere rolls all the way from one edge to the other edge of the...

Homework Statement So we have a horizontal bar. Distance = r Forces = F All numbers remain constant with the exception of the distance, denoted as r(set)() Length of bar = 1m F1 = 10N r1-1 = 0m r2-1 = .25m (behind the point of rotation) F2 = 5N r1-2 = 0.5m...

Consider the rotation of a rigid body about a fixed axis z, not passing through a principal axis of inertia of the body. The angular momentum \vec{L} has a parallel component to the z axis (called \vec{L_z}) and a component perpendicular to it (called \vec{L_n}). I have some doubts on...

Homework Statement Consider a block placed on a surface, in two different configuration, a and b. Explain the condition for which the mass is in equilibrium and describe qualitatively the rotation it follows when it falls. Homework Equations Center of mass theorem \sum F = M a_{cm} The...

Hi everyone, I have an engineering background, I'm an EE, but I know almost nothing about mechanics and that's why I'm writing here. This is the challenge: how to control the rotation of multiple discs along the same axis? Assume you have a sliced cylinder. The ideal scenario would be to...

I have a function of a 3 vector, i.e. f(+x,+y,+z) [ or for conveniance f=+++] this function is repeated 4 times where: f1 = + + + f2 = + - + f3 = - - + f4 = - + + I need a formula where i have a different vector for each function in a summation, to obtain the superposition of all 4...

I 'd like to clarify some doubts about the rotational motion around a fixed axis of a rigid body, in the case the angular momentum vector \vec {L} is not parallel to the angular velocity \vec {\omega} . In particular, consider a horizontal barbell with two equal masses m , forced to rotate...

As part of physical chemistry I am reading up group theory for molecular symmetries. I realize the way chemistry textbooks treat this must be very different from what mathematicians do. So I want to know how I take a point group, find the matrix operations and get the character table.For an C2...

I am preparing for a qualifying exam for my PhD program and am looking at some of the old tests from previous years (as supplied by the school for study/prep material). I have come across a deflection problem that has me stumped, and I might just be overthinking it. The problem:

Homework Statement We place a rubber on the edge of a rotating disk. What forces act on the rubber? At what angular velocity, why and in what direction will the rubber fly off the disk? Homework Equations http://images.tutorvista.com/cms/formulaimages/83/angular-speed-formula111.PNG The...

Homework Statement Hi! I'm trying to solve a simple problem of mechanics, but I'm getting the wrong results and I suppose I don't yet grasp the concept of instantaneous axis of rotation very well. So, a cone (see attached picture) is rolling without slipping on a plane. Vp is point P linear...

I currently have a math problem that i am so thoroughly stuck on that my brain is coming out of my ears. I am given z1 θ = 600 and R10 = [2 -2 -1] [1 2 -2]...

Homework Statement we know the mass of the moon, Mm, and the Earth's, Me, and also the initial distance between their centers as the moon orbits the earth, Rem. Now if the earth’s angular velocity about its own axis is slowing down from a initial given angular velocity, ωi to a final angular...

Homework Statement A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension : (1) angular momentum changes in direction but not...

Homework Statement Respected Physics Gurus/experts...! I am confused in the application of Kinetic energy Expression, i.e, KE = (1/2)MVCM2+(1/2)ICMω2 I had been trying out this question actually(it's pretty simple though:-p)...--- "A rigid body is made of three identical thin rods each of...

The force of gravity is what makes things on the Earth rotate with it, instead of flying off. Doesn't this mean, however, that if you were to apply an upward force on something exactly equal in magnitude to the gravitational force on the object (so the net force on it is 0), it would cease to...

There are 2 unknowns in the formula. The time period of rotation and the mass enclosed by orbit is Star. So how could we calculate the expected time period of rotation of stars in a galaxy and thus velocity of stars.

Homework Statement [/B]Hello, I am seeking help solving the following problem: find the transformation matrix that rotates a rectangular coordinate system through an angle of 120° about an axis making equal angles with the original three coordinate axes.Homework Equations none, we need to find...

Homework Statement A geostationary satellite is located at 0'N 0'E (degrees), 36000 km above a spherical Earth with radius R(earth) = 6370 km. To scan the fieldof view, the satellite rotates around its own axis(oriented parallel to the Earth's rotation axis). It records one (constant latitude)...

Hello! (Wave) A sphere with radius $10 cm$ and center $(0,0,0)$ turns around the $z$-axis with angular velocity $4$ and with such a direction that the rotation has counterclockwise direction, being seen my the positive semi-axis $z$. I want to find the rotation-vector $\omega$. Is this equal...

Why Earth rotates from West to East in southern hemisphere and East to West in northern hemisphere?? Is this true,if yes then explain please.

I've been using rotation matrices for quite some time now without fully grasping them. Whenever I tried to develop an intuitive understanding of... x' = x\cos\theta - y\sin\theta \\ y' = x\sin\theta + y \cos\theta ... I failed and gave up. I've looked at numerous online texts and videos, but...

Homework Statement Homework EquationsThe Attempt at a Solution Is it possible to solve this problem without using Hamiltonian Mechanics (just by Newtonian). My instructor expects use to solve this problem without any knowledge of any advanced classical mechanics. I tried to solve this...

So, I'm trying to plot a 3D "dipole" (an arrow with a small torus around it basically) in mathematica, and want to rotate it according to Euler angles... I use this code for the rotation matrix: rot[a, b, g] := RotationMatrix[g, {1, 0, 0}].RotationMatrix[b, {0, 1, 0}].RotationMatrix[a, {0, 0...

Hi guys, I'm having a debate with a mechanical engineer friend of mine, and I was wondering if you could help me solve it. I'm not much of a physicist, but honestly I think he might have this one wrong, I just can't remember my old physics classes well enough to calculate and be sure. The...

1. At what rate a space station 200m in diameter would have to rotate to create gravity equal to 0.7 that at the surface of earth. How fast does it spin, and how long would it take to make a complete rotation? 2. a2 = v2 / 100m T = 2pi(r) / v 3. so far: 6.867m/s2 = v2 / 100m = 26.2 m/s T =...

Public lecture on aspects of rotating astronomical objects. Covers planetary and stellar rotation, protoplanetary discs, accretion discs and galactic rotation curves. Mechanisms and observation methods.

Homework Statement A block of mass m slides down a frictionless ramp from height h above the floor. At the base of the ramp it collides and sticks to the lower end of a uniform rod, length L, mass 2m, that is suspended about a pivot at point O, about which it is free to rotate. Express...

I am aware that this could be the wrong section for this, but I wish to ask this here if you all don't mind. You all know how a sphere rolls along the ground easier than a cube, right? Well, how are the physics of motion involved in why a sphere rolls easier than a cube, or an irregular object?

I'm working with the signature ##(+,-,-,-)## and with a Minkowski space-stime Lagrangian ## \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi ## The Minkowski action is ## S_M = \int dt d^3x \mathcal{L}_M ## I should obtain the Euclidean action by Wick rotation. My...

I've noticed there are a lot of documentaries and youtube videos about what would happen if the Earth stopped spinning. However, I would like to know what would happen if the Earth kept speeding up, what would happen if it did, and the approximate maximum rotational velocity before the Earth...

Why do venus take more number of days for one complete rotation around sun than Earth when the gravitational pull towards venus is higher than Earth ?

Simple and basic question(maybe not). How are rotations performed in differential geometry ? What does the rotation matrix look like in differential geometry? Let us assume we have orthogonal set of basis vectors initially. I am looking to calculate the angle between two geodesics. Can this...

Homework Statement what's the difference between zs and hc ? in the pictuire , they are both drawn from the bottom of water to the free surface ... Homework EquationsThe Attempt at a Solution [/B]

Hello! Okay- This is a relatively simple problem, but for some reason I'm having huge difficulty with it. So I have the equation of an ellipse, x^2-6sqrt3 * xy + 7y^2 =16, which I have converted into quadratic form to get (13, -3sqrt3, -sqrt3, 7) and I need to rotate it using the normal...

In most physics introductions Euler angles(pitch, roll, yaw) are defined with respect to Cartesian coordinate system. If I chose not to use a Cartersian coordinate system but instead use a latitude, longitude and a proprietary vertical coordinate(and no back transformations to Cartersian...

Homework Statement Can anybody suggest hints on how to show that x'=xcosΘ-ysinΘ, y'=xsinΘ+ycosΘ by using the infinite string of poisson brackets? Homework Equations ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+... The Attempt at a Solution Sorry, I just can’t think of any way, substituting doesn’t work.