A tag for questions about rotational motion, including angular velocity and angular acceleration.

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Mercury's rotation, Disturbation's caused by thermodynamics

Mercury rotates sychronized like two-stroke machine. As it's solar day is 2 mercurian years.(Orbital periods) Or should we say 3:2-stroke machine, as it's Orbital period is 87.969 Earthdays, and it's ...
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88 views

Deriving some uniform circular motion equations

My question basically boils down to this. How do we derive these relationships. 1.)What is the relationship between radius and centripetal force? (inverse, but why?) 2.)What is the relationship ...
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1answer
105 views

Intuition for why friction on rolling objects is in the same direction as motion?

When we usually draw friction, it is opposite the direction of motion. However, in rotational motion problem when a cylinder is rolling on the floor, it is in the same direction as the motion. I did ...
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1answer
59 views

How would the angular velocity of the rod change if it slipped on the table?

I wanted to consider a second case of my homework assignment. We were asked to solve the question: A uniform rod of length b stands vertically upright on a horizontal plane in a position of unstable ...
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0answers
77 views

Uranus, the Physical model to change it's rotation axle

Uranus rotates pretty wierd, it's 90-degrees tilted; Why is Uranus's axis of rotation tilted? The best answer for this is; that at a distant point in its past, Uranus was struck by a very ...
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3answers
446 views

Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by: $$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$ $g$=acceleration due to gravity $\theta$=angle of inclined plane $k$=radius of gyration ...
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4answers
484 views

Earth's Kinetic energy change

Earth's rotational speed varies. I have checked the data an found following Peaks; Year 1998, 23.May, the Earth rotated in 86400.0023738 seconds. At 9.July the rotation time of the Earth was 86400....
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93 views

Can a pair of members of a “rotating system” be characterized by one value of displacement magnitude?

There seems to be a claim (cmp. Goldstein, "Classical Mechanics", eq. (4-126); or also perceptable here) that values of "velocity", and of "speed", of some participant, say $P$, can not only be ...
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2answers
42 views

Frames of Reference in a Rotational System

Imagine two concentric rings with different diameters. One is spinning within the other. There is a small gap between the outer diameter of the inner ring and the inner diameter of outer ring. From ...
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1answer
38 views

Circular Motion and Simulated Gravity

People have proposed that a spinning cylindrical shape could be used to simulate gravity. Will gravity be simulated if the cylinder is frictionless? My brain can't seem to wrap around the idea that ...
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0answers
52 views

Unruh radiation in a rotating frame

Unruh radiation normally applies to linearly accelerated frames Is there an equivalent of the Unruh thermal radiation in a frame that is spinning? I am not aware of any horizon being created from a ...
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1answer
40 views

Time in a vertical circular motion [closed]

How can I calculate the time taken to go from one point to another, in vertical circular motion? If we have radius, angle between 2 points, and initial velocity. I tried to write $\frac{dv}{dt} = g \...
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2answers
106 views

What are the Kinematics of an Irregular Tripod?

It is a common maxim (at least within the Scouting community) that a triangle is the most stable shape. In practice this means structures should have three legs whenever possible, and have cross-bars ...
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0answers
137 views

Alternate Formulation of Kinetic Energy for Lagrangian

So I have a question regarding this system: It is supposed to be a simple model of an aircraft with the fuselage idealized as a concentrated mass $M_0$ and the wings modeled as rigid bars carrying ...
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3answers
329 views

Sign of torque when rolling an object down an incline

Suppose you have an object rolling down the incline at 30 degrees. Given the point of contact is instantaneously at rest, I decided to analyse torques at that point. Therefore, the only force ...
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1answer
49 views

Velocity required for a car on a a frictionless banked surface

My textbook has clearly explained and derived a velocity that is required for a car to navigate a turn on a frictionless banked surface. I have understood it too. My doubt is about what happens when ...
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1answer
238 views

A smaller sphere purely rolling down without slipping over another larger sphere [closed]

In this question we have to find out the angular velocity of the smaller sphere about its own axis at the instant it leaves the surface of the larger sphere and it is given that the smaller sphere is ...
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0answers
27 views

Power exerted by the contact force on a wheel slipping without rolling?

I was taking an old (2008) Mechanics of materials examination, and the system is a sphere on a half circular motionless rail. We first study the motion of the sphere in the case of rolling without ...
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2answers
98 views

A Confusion in Rotational Dynamics

I am trying to analyse the following situation using classical mechanical concepts. Consider a a straight rod $AB$ of mass $M$ and length $L$ placed on a frictionless horizontal surface. A force $F$ ...
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69 views

How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the SO(3) rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As showed in f.ex. this paper, ...
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2answers
101 views

Why the bob leaves the circular path when tension in the string becomes zero [duplicate]

In vertical circular motion of a bob attached with a string, we say that the bob leaves the circular path when tension in the string becomes zero. But even when tension becomes zero there's always ...
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1answer
288 views

Is displacement in circular motion a chord or an arc?

When taking the displacement between two points along a circular path to calculate its velocity, do you take the length of a chord connecting the two points or do you take the length of the arc ...
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0answers
32 views

Angular Speed and Normal Speed

The instantaneous speed of a point along a circular path is given by $v=\omega r$, where $\omega = \frac{\Delta \theta}{\Delta t}$, $s=\Delta \theta r$, and $v=\frac{s}{t}$. However, isn’t the ...
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6answers
2k views

If the Earth is in constant motion then why do we say that an object is in a state of rest?

I got this question as my physics class homework for tomorrow. Anyone please help me out. If Earth constantly rotates and revolves, then how can we call an object in a state of rest?
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5answers
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Difference between circular motion and rotational motion

Are rotational motion and circular motion different or the same? If different then when can we say that a body is in circular motion, and when it's in rotational motion? I find several answers where ...
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0answers
38 views

Anti-centrifugal force? [duplicate]

I put some balls (denser than water) in a bucket. I took a stirring rod, and swirled the water in one direction. The water became low in the middle, and high along the edges (centrifugal force). But ...
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1answer
77 views

How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center)

A particle is revolving in horizontal a circle of radius $R$ with constant speed of $|\vec{v}|$ and constant angular velocity $\omega$. There is another observer standing inside the circle, at a ...
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2answers
94 views

Why isn't angular velocity the moment of velocity if angular momentum is moment of momentum? [closed]

Angular momentum can be defined as $L$ = $\textbf{r}$ x $m\textbf{v}$. Why is angular velocity $\omega$ then not $\textbf{r}$ x $\textbf{v}$, but instead $v = \omega \times \textbf{r}$?
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2answers
232 views

Is $v$ not always equal to $\omega r$ in angular motion?

NB:I am not asking an answer for the question quoted. I had this question given in my book: A ring of radius $R$ rolls on a horizontal ground with linear speed $v$ and angular speed $\omega =2v/R$...
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2answers
182 views

Conservation of Energy vs Conservation of Momentum in Rotational Dynamics

It is clear to me why angular momentum is always conserved, and how in some cases energy is not necessarily conserved within the system (in those cases where bodies deform, or friction is involved). ...
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0answers
21 views

Best learning of gyroscopic motion? [duplicate]

I crave to learn the nitty-gritty of attitude dynamics - namely I want to get really up close and personal with angular momentum, gyroscopic motion, non-inertial effects. I'm looking for a resource ...
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2answers
240 views

Do rotational degrees of freedom contribute to temperature?

Recently I have come across a mathematical problem where I was said to calculate the temperature increase of certain mol of N2 gas confined in a room. However, I found that there was only ...
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3answers
319 views

How do I know what variable to use for the chain rule?

In my textbook the tangential acceleration is given like this: $$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$ $$a_t=rα$$ I understand that the chain rule is applied here like this: $$a_t=\frac{dv}{dt}=\frac{...
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4answers
145 views

Why aren't all points on a rolling ball moving?

If a ball is rolling down a hill as shown, what can be said about the points indicated at that particular point in motion? (A) Point A is moving to the left, Point B is at temporarily at ...
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3answers
263 views

Why is moment of inertia for a point same as a ring

The moment of inertia of a point and ring are both $m R^2$. It is interesting that the formula for moment of inertia is exactly the same for both. Is there any physical reason why this is the case? I ...
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3answers
205 views

Gear ratio in bicycles using rotational motion

When we change the gears of the bicycle we are riding, we change the the disc we are currently at (which are located at the place where we pedal) to some other disc. This means the radius of the ...
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6answers
3k views

Conical train wheels

I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift ...
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1answer
2k views

How to Calculate Engine Torque from Wheel Torque?

Not sure if this is the right place to post - so feel free to tell me to go away :) Im trying to understand how I can use wheel torque curves to estimate the engine torque vs engine rpm relationship. ...
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1answer
375 views

How to work out the gravitational potential energy of rotating rod

I know that the kinetic energy of a rotating rod is $$ KE_{rot}=\frac12I\omega^2 $$ where $I$ is the moment of inertia. But is there some way to calculate gravitational potential energy using just ...
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1answer
44 views

Observations of erratic rotation of asteroids

An asteroid generally has an irregular shape, therefore, one would expect its rotation is quite erratic in some sense. Are there any observational examples?
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1answer
81 views

About the rotating speed of a light beam which has been reflected off a rotating mirror [closed]

A light beam generated from a source reaches a rotating mirror (x m away from the source), and is reflected off to a fixed mirror ( x m from the rotating mirror ), and again back to the rotating ...
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1answer
27 views

Using Moment of Intertia Definition to Calculate Rod's Moment of Intertia [closed]

I would like to use the moment of intertia definition to calculate the moment of inertia in this problem (from 3,000 solved problems in Physics, Schaum's Outlines): "A rod of length L is composed of ...
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2answers
756 views

Minimum velocity of the particle at the highest point [closed]

A particle of mass m is fixed to one end of a light rod of length l and rotated in a vertical circular path about its other end. What is the minimum speed of the particle at the highest point? It ...
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3answers
144 views

Rotation of center in rotational motion

For a wheel in pure rotational motion; Does the center rotate? Is there a point in wheel which do not rotate? What can we say about angular velocity of the center? From where we can start to use the ...
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4answers
5k views

A simple derivation of the Centripetal Acceleration Formula?

Could someone show me a simple and intuitive derivation of the Centripetal Acceleration Formula $a=v^2/r$, preferably one that does not involve calculus or advanced trigonometry?
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1answer
858 views

Why do we ignore rotational energy in monatomic gases? [duplicate]

I understand that the average energy of each degree of freedom in a thermodynamic system is $\frac12kT$. And so, for an ideal monatomic gas, there are three degrees of freedom associated with the ...
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2answers
163 views

Does gravity play a role in the Earth's equatorial bulge? [duplicate]

I'm trying to understand why the Earth bulges at the equator. But before looking at the Earth, which introduces gravity, I wanted to make sure I understood the shape of some rotating objects and if/...
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1answer
181 views

Kinematics of Euler angles relative to a rotating frame

I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and $\omega_F$....
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1answer
44 views

Euler Angles with respect to base body when Euler Angles with respect to another body is known

Let's say I have a fixed base body $B_0$ with a reference frame $X_0Y_0Z_0$, and two other bodies, $B_1$ and $B_2$, rotated arbitrarily with respect to this base body. Coordinate systems fixed to $B_1$...
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1answer
144 views

On the no-faster-than-light in special relativity

In the special relativity it is well established that, in the vacuum no one can ever travel faster than light, due to the relativistic velocity addition formula. Recently I saw some silly statement ...