Axis Definition and 928 Threads

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...

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...

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...

Hey, (I have already asked the question at http://physics.stackexchange.com/questions/244586/bloch-sphere-interpretation-of-rotations, I am not sure this forum's etiquette allows that!) I am trying to understand the following statement. "Suppose a single qubit has a state represented by the...

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 An anti-Helmholtz pair consists of two circular coaxial current loops each with radius R and spaced a distance R apart from each other. The loops carry current I in opposite directions. 1) Calculate the magnetic field and the magnetic field gradient along the axis at the...

Homework Statement A 14.0kg bucket is lowered vertically by a rope in which there is 163N of tension at a given instant. What is the acceleration of the bucket. Homework Equations ƩF = may The Attempt at a Solution I know how to solve this but I got it wrong because of the signs. Since the...

Homework Statement It is given that the line y= mx + c is a tangent to the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2}=1 if a^2m^2=c^2-b^2 Show that if the line y=mx+c passes through the point (5/4, 5) and is tangent to the ellipse 8x^2+3y^2=35, then c = 35/3 or 35/9 Homework EquationsThe...

Homework Statement How do I find the total charge from a material with a charge density given by \rho =10^{-9} \text{cos}\left ( \frac{z}{z_0}\right ) C/m^3 that exist between \frac{-\pi}{3}z_0<z<\frac{\pi}{3}z_0. Homework Equations None I can think of. The Attempt at a Solution Attempt #1...

I have a magnet that has a cylindrical shape, where the center is slightly larger than its outer sides. I was wondering why it beings to spin on its outer end when spun very fast (on its long edge). Whereas if its spun not too fast, it stays on its axis. I have included a photo for further...

I'd like to know if the diagonal of a rectangular thin foil is an inertial principal axis.I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a symmetry axis, so it shouldn't be a principal axis. Is it correct? So, if I consider that...

Hello, I've been trying to answering this question but my answer is always wrong. Two point charges, -9.10 μC and 21.29 μC, are placed at x = 0 cm and x = 8.00 cm, respectively. (a) At what point along the x-axis is the electric field zero? What i did: i figured that the point should be on the...

Hi, having problems with (a) here, I'll show my attempt: A1 = (0.025 * 0.05) - ((pi*0.01^2)/ 2) 1.093 x10^-3 m^2 A2 = (0.075 * 0.05) - ((pi*0.01^2)/2) = 3.593 x10^-3 m^2 A(total)*y(horz centroidal axis) = A1y1 + A2y2 y = 1.093 x10^-3 * 0.0875 + 3.593x10^-3 * 0.0375 /(4.686x10^-3) = 49.19 mm...

Homework Statement why there is no constraint of plate about a axis ? for moment about z -axis , i can have -2Bx +3By = 0 , where By and Bx = 0 which is shown in the top part of solution... Homework EquationsThe Attempt at a Solution

The above states that the velocity of point Q relative to P is represented by dr/dt. However, it also states that ∂r/∂t is the apparent velocity of Q in Pxyz. How does that make sense? I mean P is the origin of axes Pxyz so surely the velocity of point Q relative to P should be the same as the...

in this notes , the author gave that the IG is the moment of inertia calculated about an axis which is perpendicular to the page ... moment of inertia calculated about an axis which is perpendicular to the page here means id due to Ft(tangential force) only ? not include Fn ( normal force ) ...

Homework Statement A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R2 = 0.080 m and outer radius R3 = 0.090 m. The inner conductor carries current I1 = 4.4 A in one direction, and the outer...

I want to know the relationship between the optical axis direction of a crystal and the dielectric constants in different directions in an anisotropic material.

I am new to this forum. I was reading this document : http://math.kennesaw.edu/~plaval/math4490/rotgen.pdf Here the author says that from this figure http://i.stack.imgur.com/KBw9l.png that we can express $v_{\perp}$ like this : $$T (v_{\perp}) = \cos(\theta) v_{\perp} + \sin(\theta) w$$...

Homework Statement The cubic is divided into 4 parts , A, B and C, D , each with thickness of 1mm , i am sked to find thesecond moment of inertia about x -axis Homework EquationsThe Attempt at a Solution i' m using the formula Ixx = Ix +A(d^2)[/B] for part CD, Ixx = 50(1^3) / 12 + 50...

Homework Statement Calculate the moment of inertia of a uniform rigid rod of length L and mass M, about an axis perpendicular to the rod through one end. Homework Equations Parallel axis theorem: I = Icm + MD2 Long thin rod with rotation axis through centre: Icm = 1/12 ML2 Long thin rod with...

Homework Statement A uniform solid ball of mass m and radius R rolls without slipping down a plane inclined at an angle f above the horizontal. Find the frictional force and the acceleration of the center of mass.[/B]Homework Equations τ=I*α so: fs*r=I*a Mg-Fs=ma Moment of inertia for...

Homework Statement the homogenous plates shown in the figure has a mass of 10kg and is subjected to a forec and moments alonf its edges. If it is supported in the horizontal plate by means of a roller at A , a ball and a socket joint at B , and cord at C , determine the components of reaction...

Homework Statement Consider an arbitrary rigid body with an axis of rotational symmetry, which we'll call ## \hat z ## a.) Prove that the axis of symmetry is a principal axis. (b) Prove that any two directions ##\hat x## and ##\hat y ## perpendicular to ##\hat z ## and each other are also...

Can anybody suggest a free SW to simulate the behavior of a gyroscope upon adding/removing a mass in various places with respect its rotational axis and/or baricenter? It looks like it's quite complex to manually calculate or just "imagine" it. A gyro standing on a floor does behave in a...

Homework Statement Electric charge Q is uniformly distributed around a thin ring of radius "a".Find the potential at a point p on the axis of the ring at a distance x from the centre of the ring. Homework Equations ##r##=##√x^2+a^2## The Attempt at a Solution \ [/B] I just want to ask...

axis A is always normal to plane of the circle and passes thru centre of circle axis B is always parallel to plane of circle and is always parallel to y- axis of lab frame. axis B passes thru centre of the circle the infinitely long line MN always lies on the plane of the circle and passes thru...

in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body - Rotation of a rigid body about a fixed axis is defined as...

I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization, http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html and it reminded me that...

Homework Statement An astronaut on a spacewalk loses her grip on a circular garter spring (pictured below). Looking at the spring she notices that it is rotating around its axis of rotational symmetry at a rate of 300 rpm. The circumference of the rotating garter spring is 1% longer than that...

Homework Statement why the y bar is 0 ? according to the diagram , y ' has certain value , it's not 0 ! can someone help to explain ? Homework EquationsThe Attempt at a Solution

This is my attempt at understanding any real world physical effects from quantum spin. I will start with the short version first. A ... When we have a free floating electron in space is the physical orientation of the quantum spin axis locked into a fixed 3D orientation and from there can only...

Hello people, I know it seems like a silly question. In case 1, its clear that no rotation will occur around z axis. Anyhow, case number 2 is confusing me; I can't decide clearly if a rotation will occur since a moment should be generated around z axis, but in the same time, the line of the...

Homework Statement A block of mass ##m## slides down a wedge of mass ##M## and inclination ##\theta## whose surfaces are all frictionless. Find the velocity of the block when it just reaches the bottom of the wedge. Homework EquationsThe Attempt at a Solution I was told that to solve this...

Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't...

Hello, I would like to know how to calculate the drag force per unit length of an infinite cylinder with it's axis parallel to the flow field, I had read about a post here previously titled " Drag force on cylinder in parallel flow" but the slender body approximation is not valid for inifinite...

Homework Statement I can't understand why the M_0 ( M_0 = r x F)is pointing in the direction out of the paper ? Homework EquationsThe Attempt at a Solution

The question is : four masses shown in figure 12.14 (Knight 12.14) are connected by massless, rigid rods. (see attached fig) A) find the coordinates of the center of mass B) find the moment of inertia about a diagonal mass that passed through B and D so I got part a right by setting the x-y...

Homework Statement One side of a plant shelf is supported by a bracket mounted on a vertical wall by a single screw. Ignore the weight of the bracket. Find the horizontal component of the force that the screw exerts on the bracket when an 80.0 N vertical force is applied as shown Homework...

http://im54.gulfup.com/ZtJZd5.png http://im54.gulfup.com/SJgJXh.png Till now compared with other subjects that I studied by my self, linear algebra is really the toughest one :bow: Anyway, here I found a plane using characteristic eq. which really surprised me since det(M)=1, M is the matrix...

Homework Statement Two 20 lb forces are applied to a ratchet wrench down at A and up at B to loosen bolt β. Find the sum of the moments of the two forces about the axis (x) of the bolt. Homework Equations What are the moments at point A, B, and Q? How do I find the moment about the x-axis and...

Hi everybody, This is my first post, so I apologise for all the possible mistakes that I can make now and in the future. I promise that I'll learn from them! My question is the following: It's well-known the relationship between two pair of cartesian axes when a circular rotation is made...

Hi, I'm working on a project to illustrate the isometries of a tetrahedron and would like to be able to add a curved arrow around the black axis of rotation in the Manipulate display to indicate which way the solid is rotating depending if the angle is negative or positive. Here's a display of...

Homework Statement Hi, I am stuck with this homework. I have been asked to make an equation out of a diagram for V(z) using V=kQ/r equation, where z is a positive axis centred with four negative charges. Here is the diagram. 2. Relevant equation E=F/q F of point charge: F=kQq/r^2 E=kQ/r^2...

Two days ago, I have opened theme about fine-tuning on which I got good answers... Now, there is another topic, on which I have question... The reason why I am asking this question here, is because I want to get correct answer... Internet is full of trash and misinformation, and this is a...

Homework Statement (a) A satellite is initially in a geostationary orbit around the Earth, so that the satellite always remains above the same point on the Earth’s equator. Show that the radius of the orbit is ##4.22\times 10^7##(b)An engine is briefly fired in the direction of the satellite’s...

Hello. Suppose I have a coordinate system with the origin at the center of mass at rest of some rigid object and I wish to calculate the total change in angular momentum of the object with respect to it's center of mass. If I apply a torque to the object, that also happens to be an unbalanced...

Can someone correct my understanding on electromagnetic waves please; I've clearly got the wrong end of a stick somewhere, but can't figure out where my misunderstanding is! Thanks. If I draw a classic EM wave with the electric field on the up and down axis and the magnetic field at right...

Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin. Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move...

Homework Statement Two particles of mass m1 = 14 kg and m2 = 24 kg are connected by a massless rod of length 1.4 m. Find the moment of inertia of this system for rotations about the following pivot points. Assume the rotation axis is perpendicular to the rod. A) center of rod B) end of m1...