A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
Good evening,
I was wondering about how velocities transform when two successive rotations are applied. In other words, how is the transformation law between two frames which are rotating relative to another.
Lets say some particle is moving with a velocity v in an inertial frame S. If we go...
Hi, in the following video at 15:15 the twist of ##4\pi## along the ##x## red axis is "untwisted" through a continuous deformation of the path on the sphere 3D rotations space.
My concern is the following: keeping fixed the orientation in space of the start and the end of the belt, it seems...
I assume that a space station like portrayed in 2001 A Space Odyssey could either be fixed in rotation, or contra-rotating. Is there an advantage of one over the other?
So my book states torques perpendicular to the fixed axis of rotation tend to tilt the axis , however we assume sufficient restraints exist so these torques are simply ignored.
It follows that angular momentum perpendicular to axis remians constant.
(See image )
My question is that if a rod is...
This one baffles me, I still can’t get my head around it (no pun intended).
Take 2 US quarters. Put them in contact side by side. Without slippage, roll one quarter around the circumference of the other until it returns to the starting point. It requires rotating the moving quarter 2 full times...
TL;DR Summary: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?
a) Consider two rigid bodies that have a relative motion characterized by a rotation and a translation with respect to the same axis (like a bolt and a...
Hello everyone,
I am an International Baccalaureate (IB) student working on my extended essay, which is a mandated 4,000-word research paper. My chosen topic is Quaternions, a mathematical concept I find highly intriguing. The primary aim of my paper is to model the rotation of an asteroid...
For example if airplane or boat move rudder, do they always rotate around center of mass?
Or exist specific conditions when object rotate around center of mass?
I've been told that the infinitesimal change in coordinates x and y as you rotate along a hyperbola that fits the equation b(dy)^2-a(dx)^2=r takes the form δx=bwy and δy=awx, where w is a function of the angle of rotation (I'm pretty sure it's something like sinh(theta) but it wasn't clarified...
I want to ask how ##Ax^2+By^2+Cz^2+Dxy+Eyz+Fxz+Gx+Hy+Iz+J=0## can be brought to ##Ax^2+By^2+Cz^2+J=0## or ##Ax^2+By^2+Iz=0## using translation and rotation. There is no explanation in the book. What kind of translation and rotation are needed?
Thanks
I tried to solve it using the work-energy theorem.The work done to make it stand on its one vertex should be equal to the change in its kinetic energy.
I am confused what will be the value of radius here? I have seen formula of kinetic energy for rolling of circular objects.Can anyone please...
Why did he give torque number 4 zero?
It's not touching the axis of rotation and the angle 90 degrees between them.
I get this:
##\tau## = 1 - 0.8 - 0.4 + 0.4 = 0.2 (C.C.W)
I'm trying to design a mechanism to translate reciprocating motion into a 45 degree rotation.
Here's the idea:
A pin will push against the part marked in red, causing part of the desired rotation. Then, when the pin is pulled back, its interaction with the blue part will complete a 45 degree...
Hi again,
I've found interesting video.
Roller homopolar motor :
Roller Motor
Do you think the motor from 1:08 min Will self rotate in Vacuum/Space
(No other forces : Gravitational or Other type.)
Thank you in advance.
[Mentor Note: See post #10 below for an updated problem statement using LaTeX and with a better drawing]
what i want is to find the axis of rotation when the centre of gravity and point on which external force is acting is given along with the magnitude and direction of force. In the example...
Given a cartesian coordinate system with a fixed point of origin and three axes, it is a fact, that the coordinates of a point P change, when the coordinate system is rotated around its point of origin. The distance between the origin and point P is of course unaffected by such a rotation. What...
Hello everyone, i have a question, how to find wind turbine rotor rotation speed based on freewheel rotation speed of rotor (RPM)(torque = 0)? Thanks for your attention.
Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves
this paper
A. N. Lasenby, M. P. Hobson, W. E. V. Barker, "Gravitomagnetism and galaxy rotation curves: a cautionary tale" arXiv:2303.06115 (March 10, 2023).
Directly comments on Deur's theory of self-interaction...
I'm after some raw data for testing theories of dark matter in galaxies.
Basically what I want is table showing visible mass vs total mass within different radii (or, observed rotational velocity vs expected rotational velocity without dark matter). Plus error percentages. And ideally, for...
Hi everyone,
I’ve been thinking about this for a while and have done a bit of research but can’t seem to get a straight answer.
Aside from collision with another object in space, is there anything that could cause the Earth’s rotation to dramatically slow down? If a sufficiently massive object...
A solution was provided:
We take torques about point B. Note that τ = MgL/2 = Iα so α = (3g)/2L. Everything from here is straightforward.
I don't understand why in this step, you can take torque about B without accounting for a fictitious force due to the acceleration of the Rod.Thanks for...
Good afternoon,
I am working on writing a story that is set on a habitable second Moon. I suppose I could easily say it's a mild planet that splits into three main seasons and make up some story about how the first Moon appears every so often for a month of phases and then vanishes. As a...
What should I learn to make astrophysical measurements from open data?
Suppose I want to measure the rotation speed of galaxies to generate galactic rotation curves like these: https://en.wikipedia.org/wiki/Galaxy_rotation_curve
What should I do and what should I learn?
I think I should get...
Hi,
in books about machine design fundamentals, one may easily find the formulas for forces acting on the teeth of paired spur gears. They require torque as input. For example, for the tangential force: $$F=\frac{2T}{d}$$
where: ##T## - torque applied to the driven gear, ##d## - pitch diameter...
Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...
In a car we turn the wheels to steer. The wheels however are spinning about their axis of rotation when the car is in motion. Does the revolving motion of the wheels cause a force that opposes trying to rotate the wheels around the other axis to steer? How much opposition is created?
Here's...
Hello everyone!
I was wondering why can't we take a rotating body and see the linear movement that each particle moves to find the 'total linear momentum,' I imagine this quantity would be conserved, and furthermore couldn't you write the total linear momentum as a function of angular velocity...
If you put a hockey puck on a flat Ice rink, will it move due to the Earths rotation? For example, if I make a mark and measure the distance moved with a caliper, would I notice a change?
I have been trying to determine an expression for a unit vector in the direction of F for hours now.
I think the expression is supposed to look something kind of like this,
But I don't understand at all how to arrive at this expression.
Any help?
Hey, I have a question about proving Saha's equation for ionizing hydrogen atoms.
The formula is
\frac{P_{p}}{P_{H}} = \frac{k_{B} T}{P_{e}} \left(\frac{2\pi m_{e} k_{B}T}{h^2} \right)^{\frac{3}{2}}e^{\frac{-I}{k_{B} T}}
with
P_{p} pressure proton's,
P_{H} pressure hydrogen atoms,
m_{e}...
I'm not too sure how to account for both the mass and the rope at once.
I think the following are true for the two individually:
For the mass at the end, ## T = m ω^2 L ##, following from ##a = v^2/r##and ##v=ωr##.
For the rope, ##dT = ω^2 r dM##, where ##dM = λ dr## and λ is the mass per unit...
Ok. So, I already worked on this problem, and get ##m_c## = 2m/3, which is correct according to the book.
However, I also want to know the value of the tension (T) between rod A and B.
Note: Before we start working on my modified question, I want to point out that the force exerted by the...
Suppose the car is moving to the right, so if the wheels roll without slipping, they are rolling clockwise. To get the wheel to slip, a counterclockwise torque would need to be applied to cause the wheel to have some angular acceleration. If the wheel was slipping, then the bottom of the wheel...
I am doing a University lab project where I measure positions of sunspots (using images from NASA's SDO) and use them to calculate the rotation of the Sun. Currently, all is going well: I have the angular velocity of several sunspots at varying heights. However, I want to be able to find the...
Hello, so I have a question about the sense of rotation of the body.
I get the calculating part nd stuff like that. But what I don't understand is how we would determine the sense of rotation about the moment axis?
Could someone explain this to me please? (to add to this, I know that it is...
When a cyclist rides off a ‘drop’ (an abrupt step in topography, ranging from a curb to a cliff), the front wheel starts falling before the back wheel, so that by the time the back wheel comes off the drop, the bike will not be horizontal. The front wheel will be lower than the back wheel by...
figure 11.12
I need someone to explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?p.s. ##\Delta\vec{L}_{total} = \vec{L}_{f} - \vec{L}_{i} = (-rm_{d}v_{df} +...
I'm now learning about rotational motion without slipping and it's really hurting my brain to think about. Imagine a cylinder rotating on a flat plane.
I can accept that there is both translational and rotational motion. For example, a given point on the circumference of the cylinder follows a...
While revising Rotational motion, I came across a qualitative question which blew me away. Meaning I couldn't even understand the question let alone answer it😅. It has to do with these objects called spinors which as I understand are evoked in quantum mechanics and Relativity. I am attaching the...