Axis Definition and 895 Threads

I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation...

I've been having some trouble with this problem for a while. (Its not a homework or coursework problem) Its a part of an experimental set up that I'm building and this is a simplified version of it. I have a rigid rod which is hinged at a point and can pitch or heave about that location. There...

As we know that most planets has two motions around the sun , one revolving and one rotation on its own axis. So what exactly is the reason for this motions to come into play.

Homework Statement I know that potential gravitational energy is relative to the reference point that I decide to choose (like in the picture below). But then if, for instance, I set my reference point in the ceiling and my vertically down y-axis to be positive. What would the potential...

Hi, I'm currently developing an application. I'm practically done, but I have one big issue (for me). So I have 3-axis acceleration from my android device. Now I want to have the general acceleration at time t, because after that i want to calculate velocity. So, what I know: to get velocity...

Homework Statement A charge ##Q## is distributed unifromly around a thin ring of radius ##b## which lies in ##xy## plane with its centre at the origin. Locate the point on the positive ##z## axis where the electric field is strongest ? Homework Equations The Attempt at a Solution...

Homework Statement A hemispherical shell has radius ##R## and uniform charge density ##\sigma##. FInd the electric field at a point on the symmetry axis, at position ##z## relative to the center, for any ##z## value from ##-\infty## to ##\infty##. The Attempt at a Solution Let ##\theta## be...

is there a fixed angle between the fixed axis of a motor to the torque applied opposite to the motor rotation? an example is if i am using and electric screw driver to rotate a spiral screw in stable piece of wood on the floor, what should be my fixed frame if the screwdriver is I shaped and...

What causes the change in the axial tilt of the earth? Why does it change?

Homework Statement Homework EquationsThe Attempt at a Solution I understand in general the argument of the problem, the only thing which I'm not sure of is why the gravity doesn't affect the torque. My guess is that it gets canceled by the normal force that is applied on the axle but I'm...

I have never heard of a way to investigate this mathematically but I'm sure there is. How would you describe the surface area or volume of some 3-D surface formed by moving an enclosed area along a curved axis a certain distance? You could easily describe a torus by taking a circle and forming...

Hi Maybe my math/stat is very poor. I'm having trouble manipulating the standard deviation. Here's the thing. I have radar mounted on a car. For each detection, the radar returns these variables. - relative distance between the object/host vehicle in forward direction (in vehicle body-fixed...

why force parallel to the axis of rotation do not make any torque.

I need to start by saying that I'm not a physicist, nor a student of physics. I'm a translator, and my text is about rotations around the azimuthal nodal lines on the sphere. I need to find a name for a particular type of a rotation operator, which rotates the sphere around the x and y axes...

Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y2 = x; x = 2y; about the y-axis Solution...

Hello, I have a few questions regarding the osculating plane, which I understand to be the plane generated by the Principal unit tangent vector and principal unit normal vector (both are orthogonal), and the inertial Cartesian z-axis. Ultimately, I plan to understand the geometric/kinematic...

Wikipedia seems to think that a binary system is defined by a single semi-major axis, but I've seen other sources such as hyperphysics that define it using two semi-major axes. Is the semi-major axis of the system simply the average of the two?

Homework Statement A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of 3.00ˆi ms at one instant. Eight seconds later, its velocity is (8.00ˆi + 10.0ˆj) ms. Assuming...

Homework Statement Consider the beam shown in (Figure 1) . Suppose that a = 15 in. , b = 8 in. , c = 1 in., and d = 4 in. Determine the moment of inertia for the beam's cross-sectional area about the x axis...

Homework Statement The moment of inertia for a perpendicular axis through the center of a uniform, thin, rectangular metal sheet with sides a and b is (1/12)M(a2 + b2). What is the moment of inertia if the axis is through a corner? The answer is given as this was a powerpoint lecture and it...

So imagine you have two disks, and from your perspective one is spinning on its vertical axis and the other one is spinning on its horizontal axis. What do you call that? And what would it mean to "spin at the opposite polarity" if such a sentence makes any sense at all? Thank you! Sorry if...

Homework Statement A thin uniform rod of length l and mass m is constrained to rotate with constant angular velocity omega about an axis passing through the center O of the rod and making an angle alpha with the rod. a) Show the the angular momentum L about O is perpendicular to the rod and is...

If you spin up a flywheel by applying torque somewhere else on its axle, you are transferring energy along the axle from the point where the torque is being applied to the flywheel, which effectively adds to the mass of the flywheel. This means rather counter-intuitively that a tiny force has...

Hello, I am trying to make a graph on excel 2013 with two y axes, and the internet says I should click on the "Layout" tab under the Chart Tools tab, but I do not have that tab. How do I do this?

The figure shows a section of three long charged cylinders centered on the same axis. Central cylinder A has a uniform charge qA= +3q0. What are the charges of qb and qc if E is 0 on point > a) 1 ( between A & B ) b) 2 ( between B & C ) c) 3 ( out side the cylinders ) My solutions were based on...

Suppose we have do a curl of two 2-d vectors... we get the 3rd axis about which it is rotating. But when we do the curl of two 3-d vectors.. we get a answer like x-y plane is rotating wrt z axis, y-z plane rotating wrt to x-axis and similarly x-z plane rotating wrt to y axis. My question is...

Homework Statement Homework Equations Parallel axis theorem: Ip = Icm + Md^2 Icm = I = ML²/12 + 2 * mr² 3. The attempt Ip = Icm + Md^2 ==> wrong I = Md^2 ==> right Why don't I need to add "Icm"? Thanks.

Homework Statement Compute the force between two identical dipoles. See Problem P63 on page 544 to set up the problem. Explain why this result makes sense by comparing it to the force between two point charges and the force between a point charge and a dipole, in terms of the relationship to...

I remember my teacher saying it to be the axis along the centre of mass but the centre of mass has all the mass concentrated in it and hence moment of inertia should increase as moment of inertia is proportional to mass?

Homework Statement Calculating the moment of force F about the axis isn't hard; how do I determine how to produce the maximum moment? Homework Equations Maxis = ûaxis ⋅ (r×F) F = 30N (This doesn't change at all during the problem) The Attempt at a Solution I would guess that since the...

I'm trying to map out local space using Astrosynthesis and have been looking up stellar data online. When I come to companion stars, rather than use the RA and Dec for the star - only its position at the time of observation - I use the orbital data relative to the primary. One of the...

Hi (I hope this is the right place to post this - sorry if it's not) Say I have a line (in the graphic is shown a 10mm but it could be any length) and it rotates around a point at one end. What is the formula to get the length along the x-axis directly under the other end of the line. In the...

Hey guys, first of all, this isn't a homework question, I just want to know why the results are what they are. I've been trying t obtain the same numbers using moment equilibrium but they still don't match. This is the example: W are the forces applied by the gears in force-pounds. The gears...

Homework Statement A force F is applied over axis M-N in the such shown position. Both of points A and B are not fixed, and can slides inside the black fixed circle. will the applied force (in the shown position) cause the axis M-N to rotate ? if it is not rotating, then what modification...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. (Use disk method) $$ xy = 3, y = 1, y = 4, x = 5 $$ Homework Equations [/B] The formula using for disk method is of the form: $$ \pi \int...

Hello guys, I'm doing my physics coursework on kepler's third law and I'm finding the minimum mass and semi-major axis of a unknown planet. I have the following data: Stellar mass Mstar = 1.31 ± 0.05 Msun Orbital period P = 2.243752 ± 0.00005 days Radial velocity semi-amplitude: V = 993.0 ±...

I googled this question and found sources which claimed the moon slowly, over about 27 days, rotates on its axis. Yet wouldn't rotating at a speed so that about 40% of the moon never faces the Earth suggest that it is rotating around an axis somewhere inside of the Earth, rather than inside of...

Homework Statement You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.700 kg . 1What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? Express...

Hi PF! I am running matlab2tikz and it is working great. However, is there a way to control what the axis look like? Right now my axis have an entire square. Anyone know a way to edit this in the tikZ file? I've attached two figures, the non-square one is what I would like my axis to look like...

Homework Statement We have a fluid with density ρ which is rotating about the z-axis with angular velocity ω. Where should a unit square, call it S, be placed in the yz-plane such that there is zero net amount of fluid flowing through it? Homework Equations...

Firstly, let me explain that I am mostly inept at mathematics. Piecing together the required information is becoming a real challenge because of that. I am motorizing a dobsonian telescope. I have read many accounts of success and the steps involved. The places where detail is commonly left out...

Homework Statement A thin rod of length l and mass M rotates about a vertical axis through its center with angular velocity ω. The rod makes an angle φ with the rotation axis. Determine the magnitude and direction of L (angular momentum). So we're given: mass - M, length - l, angular velocity...

Given $$x_1^2 -y^2=a^2, \ \ x_2=a+h$$ Or $$x_1=\sqrt{a^2+y^2}$$ Find Volume about the $y$-axis So... $$\pi\int_{a}^{h} \left(x_2^2-x_1^2\right)\,dy$$ Actually I am clueless?!

Find volume bounded by $$x=2\sqrt{y},\ \ x=0, \ \ y=9 $$ About the y axis So.. $$\pi\int_{0}^{9}(2\sqrt{y})^2 \,dy = 160\pi$$ But the book answer is $162\pi$ ?

Given only the triaxial stresses: ax = 10 MPa (along [100]), ay = 10 MPa (along [010]), and ax = -30 MPa (along [001]), what is now the components of stresses in rotated axis? so based on the equation aT = [L][a][LT] let aT the components of stress of rotated axis, L the direction cosine, LT...

Is there a preferred axis in cosmology, if there is what is the origin? arXiv:1604.05484 [pdf, other] Preferred axis in cosmology Wen Zhao, Larissa Santos Comments: 21 pages, 9 figures, 8 tables, invited review Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity...

When cosmologists talk of the "axis of evil" are they referring to the hemispheric power asymmetry or is that considered a different anomaly?

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...