# Rotation Definition and 235 Discussions

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.

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1. ### I Slowing Earth’s Rotation

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...
2. ### Questions about a habitable second moon

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...
3. ### Finding tension as a function of distance from the center of rotation

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...
4. ### Tension between two rigid bodies

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...
5. ### Forces when car wheels "lay rubber"

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...
6. ### Disk and Stick Collision

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} =...
7. ### I A Question on Spinors in a High school textbook

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...
8. ### I How to numerically find control settings given the expected acceleration? (lunar lander)

I'm currently working on a pet project which is similar to the OpenAI Lunar Lander v2 (hence the problem is in a 2D context), and seeking help for a sub-problem that's been blocking me for a while. At any instant of time, I'm to find Fe: magnitude of main engine thrust, must be >0 Fs...
9. ### B Calculating the torque needed to rotate a drum

Imagine this: You have a drum with a radius of 12cm, around that drum is a toothed belt which is connected to a motor. The drum weighs 10kg The motor should be placed under the drum How would I calculate the amount of torque needed to rotate the drum I don't have any idea how to calculate this...
10. ### Mass m sliding without friction inside a rotating tube

1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$ 2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this. 3) In ##R_0## the...
11. ### How long does it take for the disk to stop rotating?

Question : Solution attempt : for
12. ### How would one estimate the rotation period of a star from its spectrum

The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
13. ### Find the frictional force acting on a solid cylinder

This was the answer key provided: My questions are the following: if the force required for rotational equilibrium is more than the limiting static friction, then the body will rotate aka slip over the surface. When it slips, the frictional force will be kinetic and not static, right? If I...
14. ### Conservation of energy in rotating bodies

The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder. To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder). However, I viewed the cylinder as rotating...
15. ### Two rotating coaxial drums and sand transfering between them (Kleppner)

The solution is simple by noting that the total angular momentum of the system is constant. (Though I overlooked this) Instead, I went ahead analyzing the individual angular momentum of both drums. Let ##L_a## and ##L_b## be the angular momentum respectively. ##M_a##, ##M_b## be the...

30. ### Can you feel planet rotation?

It's often said that you don't feel Earth rotation because the gravity acts against the centrifugal force. Of course this is true but also your body is turned around once each 24 hours. So I wonder on a planet which is rotating once each 3 seconds and has same g=9,81: Would you feel the rotation?
31. ### An isolated object can rotate only about its center of mass

I was talking to someone about the equilibrium of fluids and we reached at some stage where we had to prove that in an external field the translational forces add to zero along with moments (torques) should also add to zero. The first one was quite easy but during the discussion of second...
32. ### About the Moment of Inertia

Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects. The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment...

34. ### Rotation and spring force exercise

Summary:: Calculating the inclination angle A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...
35. ### Invariance of a spin singlet under rotation

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...
36. ### Translational and rotational velocity

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
37. ### Newton's Second Law for Translation and Rotation

Answer choices: N2L for Translation, N2L for Rotation, Both, Either 1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. My solution = N2L for rotation 2. You are asked to find the angular acceleration of a low-friction pulley due to...
38. ### A uniform rod allowed to rotate about an axis and then it breaks

A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...
39. ### Tension in a rotating rod at various places

(The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite). I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...
40. ### The Bizarre Behavior of Rotating Bodies, Explained

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
41. ### Yo-yo on an accelerating conveyor belt

First off, I was wondering if the acceleration of the conveyor belt can be considered a force. And I'm not exactly sure how to use Newton's second law if the object of the forces is itself on an accelerating surface. Also, I don't know whether it rolls with or without slipping. I thought I could...
42. ### Auto/Motor Swirl push maker DIY

Hi Everyone! I am trying to a DIY project to make a food maker. I am 50% succeeded with that and need help for the remaining 50%. The idea is to produce the output shown in the first image. That food is made with a flour. So I have the setup a pressing machine shown in image2. In this I was...
43. ### A basic question about rotation

Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure. Find the maximum velocity the ring must roll so that it doesn't...
44. ### Rotating with slipping to rotating without slipping?

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.
45. ### How to stop a steering wheel using an electric motor?

Problem Statement: i have a steering wheel mounted on an electric motor, and i want to stop the driver from going beyond a certain angle. i can read the torque applied by the driver, and the steering wheel angular velocity as well. how can i stop the steering wheel, without sending it harshely...
46. ### Problem Concerning Rotational Kinetic Energy

For parts A and B I used energy to find the vcom and omega, but that won’t work for C. I have an answer by combining the three formulas that use acceleration above. My answer for alpha=-5g/3r. The next two are easily solvable if you find C, but I still feel like I’m missing something. Any help...
47. ### A Ideas for determining the volume of a rotating object

Hello everybody, I am currently working on an experiment investigating the formation of planets. I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together). From the imagery I can see those agglomerates which are build up by smaller...
48. ### A question about magnetism that causes a wheel-loop to rotate

This question is from 1977 AP Physics C so I suppose it would be clear enough, but I am confused about question c. Question a is easy (it rotates counterclockwise), question b too (Στ=6*rxF=6*r x (I*i x B)=0.06). Question C is where I am stuck. The diagram provided with the question looks like...
49. ### Motion in a vertical loop

$$mg(0.45) = mg(R + R \cdot cos(\frac{π}{3})) + \frac{1}{2}mv^2$$ $$v^2 = g(0.9 - 3R)$$ The centripetal acceleration during the "flying through air" will be given by gravity $$mg \cdot cos(\frac{\pi}{3}) = \frac{mv^2}{r}$$ $$R = \frac{1.8}{5}$$ But my book says $$R = \frac{1}{5}$$
50. ### How to calculate angular speed?

Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...