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# Questions tagged [rotational-kinematics]

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

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### If we take a sufficiently large axle for a wheel then is it possible that the top of the wheel would have thrice the velocity of its axle?

I recently learnt that the top of a wheel has velocity twice that of its axle. In all such cases of why this is so the axle is always considered to be very small in comparison to the wheel. Thus, I ...
1 vote
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### Rotating Tank of Charged Liquid

Consider a long rectangular tank of dimensions a×b, where a≫b, that is rotating at a constant angular velocity and filled with an incompressible charged fluid. How would one find an equation ...
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### Linear approximation of the magnetic dipole field

Summary: using 3 angles to represent a magnetic dipole's orientation is redundant because the rotation around the $z$-axis of the dipole does not change the magnetic field, there are only 2 DOFs for ...
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1 answer
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### Does spinning the umbrella slow down the fall more?

Ignoring its structural weakness, if you jump from some height and use an umbrella to slow down the fall, would making it spin while you're falling affect the speed in any way?
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### Relative motion between two points on a rotating disc

Consider two children A and B sitting on diametrically opposite points of a merry go round rotating about its centre. Suppose A and B are facing each other. As seen from A, B never seems to move and ...
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### Linear velocity on a circle

Consider a ball rotating around the z-axis with constant angular velocity $\vec{\omega}$, then the linear velocity $\vec{v}$ is given by $\vec{v} = \vec{\omega} \times \vec{r}$. It is easy to ...
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### Closed form solution for the linear acceleration of a particle on 3D rotating object given momentum and MoI?

Is there a closed-form solution for the linear acceleration of a particle on a rigid body undergoing some arbitrary rotation in 3D with no external forces, given its angular momentum vector and its ...
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3 votes
2 answers
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### Vector Associated with Rotation Matrix

I am reading the $3^{\mathrm{rd}}$ edition of Goldstein's Classical Mechanics, and on p. 165 in Chapter 4 around eqs. (4.67)-(4.68), the authors derive the transformation matrix corresponding to a ...
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### Does relative motion allow for speeds $>c$?

If motion is relative, (so if X was stationary and Y was moving at v m/s, we could think of this as Y being stationary and X moving at -v m/s), could we not create a scenario in which a stationary ...
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### Wrong concept in rolling question

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct? ...
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### Why need the extra definitions for rotational motion?

Why do we need to define things like angular momentum, torque, etc.? I want to do everything with fundamental quantities. The conservation of angular momentum relies on the conservation of linear ...
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### Energy loss due to friction in Rolling Motion

I understand why rolling motion does no work. My (possibly imprecise) summary of the answer is that net work done is zero. And the role of friction is to convert translational kinetic energy into ...
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### Created a resource to help solve a problem I was having in a lab. Can I publish it?

I had to complete a lab for school assessing the accuracy and precision of calculating a triangular prism’s moment of inertia using a trifilar pendulum. When I wanted to compare my lab results to ...
3 votes
1 answer
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### Speed at which the Moon moves past a point on Earth's surface?

I'm trying to calculate how fast a point on the surface of the Moon is moving past a point on the surface of the Earth (I assume a point on the equator of each for simplicity). I know the Earth is ...
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### Angular velocity relative to some frame

In "Introduction to Robotics" by John Craig, we have the following statement: The vector ${}^A \Omega_B$ describes the angular velocity of $B$ with respect to $A$, and ${}^C({}^A \Omega_B)$ ...
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### Should the rotary vane damper torque be less than the load torque?

The rated torque of a rotary vane damper should be less than or more than the load torque? In my opinion, if the rated torque is greater than the load torque of the damper, then I believe my ...
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### Understanding the meaning of the directions of $\vec\omega$ and $\vec{L}$

I'm struggling with some basic intuition regarding the angular velocity $\vec\omega$ and angular momentum $\vec{L}$ vectors, for any arbitrary motion. Specifically, I'm trying to figure out what the ...
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### Combined KE for an object rotating about a point other than COM

I know the KE equation for combined translational and rotational motion, which is $K=Mv^2/2+I\omega^2/2$, and here $v$ is the velocity of COM and $I$ is the moment of inertia about the COM. But what ...
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### Understanding angular velocity $\omega$ as a vector

I would like to validate my understanding of angular velocity as a vector. Suppose we have a particle $P$ moving around in $3D$ space in some arbitrary way. At any given point in time, we would like ...
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1 answer
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### Rotation of a sphere on two different axes

You have a small globe, which is mounted so that it can spin on the polar axis and can be spun about a horizontal axis (so that the south pole can be on top). Give the globe a quick spin about the ...
3 votes
2 answers
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### Can the same rough surface provide frictional force on opposite directions for translation and rotation of a sphere under a tangential external force?

I came across a question which says: "A force $F$ acts tangentially at the highest point of a sphere of mass m kept on a rough horizontal plane. If the rolls without slipping , find the ...
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### Angular Velocity and Angular acceleration when the position vector is changing

I was watching a lecture about circular motion and how angular velocity and angular acceleration differ if origin changes.The teacher at 9:10 says that we cannot apply the formula $a=rα$ as position ...
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### Relative angular acceleration

Let us consider a particle which is rotating in a circle of radius $R$ with a uniform angular velocity of $ω$. We are observing this particle from a frame rotating about the same axis with uniform ...
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### Is the angular acceleration and the resultant acceleration the same thing? [closed]

Is the angular acceleration and the resultant acceleration of tangential and centripetal acceleration the same thing in non-uniform rotational motion? If not, what's the difference?
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### What if an object is rotating near light speed? [duplicate]

lets say that we have a cube made of say 1kg, and using some means, managed to impart enough angular momentum to make it rotate at the speed of light or at least 99% of light speed. ignoring the fact ...
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### Is the radius equal to length/radians? [closed]

Is the radius equal to the length/radians. Since the circumference is 2 pi times r and radians of an entire circle is 2 pi r should be equal to lentgh/radians I needed this proof to understand why we ...
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1 answer
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### Rotating fluid shape with its own gravity

Hi almost every student knows the rotating bucket with a fluid problem as described here: Fluid in a rotating cylinder I wanted to do the same for a rotating fluid in free fall (like in the ISS) to ...
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### Absolute Angular Velocity - How to use?

From my dynamics course, we were introduced to the so-called absolute angular velocity of a rigid body. Below is a short diagram: The following equation for the velocity of point P on a rigid body is ...
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### Assistance in writing the rotational constraints of a spool, in rotational dynamics

I came across a very interesting problem involving rotational dynamics, from the series of Cengage Physics books, which was asked in an Indian competitive exam called KVPY. Write the constraint ...
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### How to measure Angular Velocity observed from A non-stationary frame?

A stationary observer observes a rotating disc with radius 1 at angular velocy w. Let's say this disc is centered at origin in xy plane (all angular Velocity mentioned in this question is around the ...
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### Is angular velocity and angular acceleration independent of translating frame

[CONSIDERING ALL BODY RIGID] So think of a body which is rotating if I see it from a rotating frame,let's say with same angular velocity then the body will appear rest to the frame , so will have zero ...
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