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

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6
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1answer
4k views

Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
0
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0answers
38 views

Why do linear momentum and angular momentum have to be conserved in ground frame only?

According the Newton's second law of translational and rotational motion respectively if the net external force /torque acting on a body is zero then the linear/angluar momentum is a constant . So ...
0
votes
1answer
93 views

Physics related derivation of equation of cycloid

So I was trying to find the path traversed by a point on the rim of a rolling disc. I eventually landed up at an equation but when I went to check it out in the internet, I couldn't find any similar ...
1
vote
1answer
33 views

Simplified rolling tire problem - hollow shell vs solid?

First off, I don't understand the math formatting thing on here, but none of these formulae are too complicated. Take a tire rolling down a hill with angle t and distance d. Modeling it as a hollow ...
0
votes
1answer
58 views

Speed of a point on a concentric disk setup

I have been really solving this question that my friend and I had thought of while discussing about speed of light. Imagine there is a set-up where there is a light source that is surrounded by a ...
0
votes
3answers
186 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 ...
0
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0answers
124 views

Tension in a rod rotating about a fixed point

A rod of mass $m$ and length $l$ is rising about a fixed point in the ceiling with an angular velocity $\omega$ as shown in the figure. Now, on taking a small element on the rod, the net tension ...
2
votes
1answer
176 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 ...
1
vote
1answer
81 views

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 ...
0
votes
1answer
73 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 ...
7
votes
4answers
468 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 ...
0
votes
1answer
98 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 ...
1
vote
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 ...
1
vote
0answers
76 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 ...
3
votes
2answers
92 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 ...
0
votes
1answer
341 views

On application of angular momentum conservation laws

Consider a situation like this: a massless ring is kept fixed at rest on a horizontal plane. A massless thin string attached at its one end to a point on the circumference of the ring while its other ...
0
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0answers
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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3answers
20k views

Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
0
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2answers
41 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 ...
0
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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 ...
2
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0answers
47 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 ...
-2
votes
1answer
39 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 ...
0
votes
1answer
149 views

Determine coordinate system for rotating wheel

I am having trouble writing down the coordinate systems for a problem. In particular, I'm not sure how to figure out the translational acceleration of the moving coordinate system relative to the ...
4
votes
1answer
7k views

Why is the velocity on the top of a wheel twice the velocity of its axle?

When a wheel is rolling, not skidding, and its axle moves at velocity $\vec{v}$, then a point on the top of its circumference will move at velocity $2\vec{v}$, shown below. I really don't ...
2
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3answers
314 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 ...
1
vote
1answer
212 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 ...
0
votes
1answer
48 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 ...
2
votes
2answers
96 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 $F$ ...
0
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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 ...
6
votes
0answers
64 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, ...
-3
votes
2answers
99 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 ...
9
votes
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?
1
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2answers
694 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? ...
0
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0answers
31 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 ...
1
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0answers
37 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 ...
1
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1answer
72 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 ...
0
votes
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 $v = \omega \times \textbf{r}$?
1
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2answers
213 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 ...
0
votes
2answers
174 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). ...
0
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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 ...
0
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2answers
210 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 ...
2
votes
3answers
316 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: ...
3
votes
3answers
9k views

Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion

The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is ...
1
vote
4answers
139 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 ...
3
votes
7answers
6k views

The Earth is spinning, so why don't we jump and land on a different location?

I know there are similar questions in stackexchange but i think it's different and detailed. The earth is spinning 465 meters/second so why don't we jump and land on a different location ? I have ...
0
votes
3answers
251 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 ...
20
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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 ...
22
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8answers
30k views

Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)?

Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)? I have completely no idea and I am inquiring about this as it is an ...
4
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2answers
448 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = ...