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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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Is rotation absolute? [duplicate]

I was reading an article that rotation instead of linear motion is absolute. Can anyone explain why? Shouldn't an observer (A) moving in a circle around a point in an object that rotates (with respect ...
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Inertial frames and Rotation: shooting up a ball from a rotating platform

A short cylindrical tube is fixated in a horizontal platform and shoots a ball vertically in such a way that it falls back into the tube. Now imagine that the platform is spinning with a certain ...
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Pendulum moving in linear motion [closed]

Given a diagram below, the linear velocity of the point of rotation is v_linear and the angle that the tension line makes with vertical axis is theta, and its angular velocity theta dot. Assuming ...
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1answer
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Kinetic energy of disk rotating around axis parallel to the one through its center [duplicate]

Given the situation shown in the figure below. A thin disk with mass m and radius r is rigidly connected to one end of a massless rod with length l at its centre, with the other end of the rod ...
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Rotational dynamics regarding uniform rod

Is centripetal force present in rotating objects? I just solved a question in which an uniform rod rotates about a vertical axis with its one end pivoted. The angular acceleration is found by just ...
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Is an inertial force needed to be added to second Newton's law when transforming from cartesian to cylindrical coordinates?

Let's consider I have a particle moving on the $x,y$ plane. On this particle acts the Lorentz force, however it does not necessary perform a rotation by the axes origin $(x,y)=(0,0)$. I would like to ...
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1answer
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Can I theoretically completely convert the kinetic energy of a bullet to rotational energy of a disc, when the bullet hits it tangentially?

Will the kinetic energy of bullet be converted to rotational energy of disc(assume the bullet gets stuck to the disc). Let me assume that disc is mounted on a car standing on a frictionless surface. ...
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Where does it getting wrong , when using $v^2 - u^2 = 2as $ down the incline, for different object having different moment of inertia?

Well, Consider a situation there is a sphere and a ring, of same mass $M$ and radius $R$. They both starts rolling down the inclined plane. We know moments of them as well, $$I_\text{sphere}=\frac{2}{...
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Stone skipping does spinning help?

I have tried to hurl a stone with some added rotation and it performed slightly better but I have great difficulty replicating this feat for consistency, my question is should I add angular momentum ...
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1answer
46 views

Finding velocity of a rolling disc down a slope

When finding the velocity of a rolling disc using newton's second law method we need to take into account the friction. We use $$ mg \sin(\theta) - F = ma $$ and $$ Fr = I \alpha$$ $$I = \dfrac{mr^2}...
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1answer
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Is it easier to balance a free-standing ladder when standing on the bottom step or the top step?

This video shows someone climbing a ladder not resting against a wall: https://youtu.be/bWOSbEtDAas . I was wondering if it's harder to balance the ladder when you're standing near the bottom, or ...
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Why should the friction between two disks be zero when there velocity is same? [duplicate]

In this video here, Walter Lewin mentions two discs of different radius $r_1$ and $r_2$, of the same density, where the first disk is initially rotating, while the second is at rest. In the videos ...
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A question on rigid body dynamics.

What is the intuition for angular momentum of a point mass relative to a inertial point? Does the definition of angular momentum of a point mass holds true in non inertial reference frame? How?
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1answer
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A problem on determining coriolis force on frames

First of all I am defining x axis in east of object and y to be in the north of object . Let us suppose a body is falling from a height; then after falling a certain height indeed gain some velocity ...
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1answer
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How can a body be rotating when it's translating?

How does a translating object (with constant velocity) seems to have a rotatory effect when viewed from a point not in its line of motion?
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Is one side of earth faster at night and slower at daytime?

I'm reading Physics for Entertainment by Yakov Perelman and in it he says under "When we move around the sun faster" that at midnight the speed of the rotation of the earth is added to that of earth's ...
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1answer
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Gyroscopic precession on a friction-less surface

I am having trouble understanding the total energy for a heavy spinning symmetric top (Gyroscope) on a friction-less surface. I am trying to understand it via the Lagrangian of the gyroscope. My ...
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2answers
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Can torque about an axis be defined for non-rigid bodies?

I've assumed a body in which points are radially moving outward(say).$$\vec F_i=m_i\vec a_i$$ where $\vec a_i = \vec \alpha_i \times \vec r_i$. Considering a point $O$ about which torque will be ...
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1answer
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What is the EMF in a bar rotating around any point?

The problem of a bar (or rod) of length $l$ rotating around one of its ends in a magnetic field of magnitude $B$ is very well known. The induced emf is $\frac{1}{2}B\omega l^2$, where $\omega$ is the ...
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1answer
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How can I calculate the power required to make an air turbine spin at a constant rpm?

Say I have an air turbine with diameter $d$, number of blades $N$, and moment of inertia $\frac {d^{2}*M_{Blade}^{**1}}{4}$ (at the tip of the blade). How do I calculate the power required to spin ...
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1answer
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How does horizontal speed affect rotational velocity?

Attaching 'spinners' to a car causes a rim to spin when stopped at a red light. When the car picks up speed again, the spinners slow down to a halt. Why is this?
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Why can Different Particles have Different Velocities when Rotating

When a rigid object moves linearly, all particles within the object must have the same velocity or the object will split apart. However, when dealing with a rotating object, we know that tangential ...
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1answer
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Difference between the angular momentum for a mass following a trajectory and a mass rotating around a rotational center

I struggle to find a satisfying reason and formulation, why for a point mass, that is fixed in a rotational system and the radius is changed (like pulling on a string with a small ball rotating ...
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Does the hinge reaction do any work?

I was doing some questions in rotational mechanics and I am not able to understand the concept behind hinge reaction which acts on a rod suspended at a point. I am taking a simple example here. Let's ...
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3answers
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Cylinder vs cylinder of double the radius roll down an incline plane, which one wins?

A solid cylinder and another solid cylinder with the same mass but double the radius start at the same height on an incline plane with height h and roll without slipping. Consider the cylinders as ...
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If the Sun moves across the ground at 0.25 nautical miles per second, why do shadows move very much slower? [closed]

This title has been discussed previously on this site here. Question: Shadows from the sun moves fairly slow across the ground. Maybe a centimeter per sec. however, I calculated that the sun is ...
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1answer
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Is Radial Acceleration really Constant? [closed]

When a charged particle undergoes deflection in a Magnetic Field it follows a curved path while moving with some velocity. We calculate the deflection by finding the radial acceleration and time spent ...
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1answer
57 views

Perpendicular weight force on an object that is tipping over [closed]

I'm currently working on a problem I can't seem to find an answer to. I have an object that is hanging over a cliff. This object is exactly 12m in length, and it starts off in equilibrium (6m over the ...
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Angular momentum, velocity and center of mass

I have a small question. Assuming I hold a given stick A with weight mA, which has a Weight B with mass mB attached to it, start rotating and release at any point. The general movement would be ...
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2answers
78 views

Rolling Without Slipping and Rotational Energy

I'm a little confused. Translational energy and rotational energy add separately, according to my textbook, to give the total kinetic energy of a moving object. That means that for a disk ...
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Solid rotates about $n$ axes

A solid rotates about $n$ axes intersecting at one point. The absolute value of angular velocities of each rotation $|\boldsymbol{\omega}_k|\,(k=1,..,n)$ are constant. Find the angular velocity vector ...
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1answer
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How to get rotation components in each axis?

To explain what I mean let's say I have an object that is moving and I know its speed and direction (angle). I can get the X and Y components of speed using ...
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1answer
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Conservation of energy in rotational motion [duplicate]

Suppose a boy is standing on a platform which is free to rotate about an axis passing through its center. The Kinetic energy of the boy and the platform is K. If the boy stretches his hands so that ...
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1answer
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How can I determine the rotation point and the rotation axis if I know two velocities of a rigid body?

In case of a "2D" rigid body I can find a vector $\vec{r}_1$ that is perpendicular to the velocity $\vec{v}_1$ at point $p_1$, $\vec{r}_1\perp \vec{v}_1$ at point $p_1$, and the same for point $p_2$, ...
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1answer
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Noob question about centripetal acceleration

This is a very simple question, but one that has been bugging me since long. Consider a rod of length $L$ and mass $m$ to be hinged at one end. It is vertical initially. It is displaced slightly from ...
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Rigid bar on a pivot

Say we have a solid bar in space. It is on a pivot, the pivot being right at the bar's center of mass There is a massless rocket pushing on one end of it, making it spin, faster and faster. Suddenly,...
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Rotating table problem and problem solving methodology [closed]

Here is the question 'A table with smooth horizontal surface is turning at an angular speed ω about its axis. A groove is made on the surface along the radius and a particle is gently placed at a ...
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1answer
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The path of a disk/cylinder with translation and rotation [closed]

The conditions: We have a regular disc of mass $\mathrm{M}$ and radius $\mathrm{R}$. It is placed on a horizontal plane with friction (which is constant throughout). It is then given an initial ...
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Rate of change of heading in terms of normal acceleration and air speed

Let's say an aircraft is traveling with speed $|\mathbf v|$ with respect to an inertial frame. The aircraft is able to execute turns by producing an acceleration $\mathbf a$ that is normal to $\mathbf ...
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1answer
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Relation between rotation vector derivative and angular velocity when the rotation angle is constant

$\def\va{\vec{\alpha}} \def\vw{\vec{\omega}} \def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
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3answers
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Multiple Centers of Mass [closed]

This may sound like a trivial question, but I am wondering: is it possible for there to be multiple centers of mass? And if it isn't, why? For example, take some arbitrary 3-Dimensional object, ...
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Formalism to describe oriented object moving through space

After reading about rotation formalisms what I am after is the formalism to describe how an oriented object moves through space. $\def\R\{\mathbb{R}} \def\Rx{\R^3}$ With $s: \R\to\Rx$ one can ...
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1answer
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Angular Momentum of Object Accelerating in a Straight Line [closed]

I've been given an object with $r(t)=|v|t\hat{x}+b\hat{y}$ and been asked to find the specific angular momentum and see if angular momentum is conserved. I found $L=r\times p=-m|v|b\hat{z}$. My ...
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1answer
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Why is acceleration in the rotating system zero?

Given a circular body that rotates around itself and there is a band(or iron line) that connects between the Cartesian coordinate system and its Perimeter, on the band, there is an ant that walking ...
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1answer
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Rotational Kinematics and Angular Velocity Vector Transformation

Say we have a rigid body with a body-fixed coordinate system XYZ and an inertial coordinate system (North - East - Down) XoYoZo. If we use the x-y-z convention and rotate the body fixed frame first ...
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1answer
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Velocity in rotating frame projected onto axis in inertial frame

I want to look at the projection of the velocity of a particle in the rotating frame onto an axis in the inertial frame as a function of time. For example, I am calculating \begin{equation} \frac{d\...
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1answer
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An interesting problem from circular motion [closed]

Consider this situation: Two individuals are seating side by side on a Merry-go-Round moving with angular velocity $\omega$) seats they are just seating next to one another. Now the person A is ...
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1answer
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Calculating angular velocity of rolling object with just gravity?

From what I have learned, you can calculate what the angular velocity of an object will be based on its potential energy. Say there is a situation where: acceleration due to gravity = 10 m/s² ...
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3answers
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Why do vehicles with a higher center of mass roll more easily considering that they have a higher moment of inertia?

It is a well known fact that cars with a higher center of mass roll over more easily, but why is this true considering that higher center of mass = higher moment of inertia? I understand that the ...