Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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Find the time when tangential acceleration is equal to radial acceleration [on hold]
A particle begins to move along a circular path of radius R with a constant magnitude tangential acceleration of $a_t$. After time $t$ it's the centripetal acceleration is equal in magnitude to ...
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1answer
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Rotating Torque
I have started learning about rotating torque from Berkely Physics Course-1. I came across the bead on massless rod setup as shown in the figure below.
Since omega and angular momentum are not ...
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Addition theorem for angular velocity --> “addition theorem for angles”
I'm wondering if it is possible to go from the addition theorem for angular velocity to the "addition theorem for angles".
For example (I used the same notations of Wiki):
$${^N\!\omega^B} = {^N\!\...
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Why do office chairs rotate when pushed/pulled out?
A common source of frustration when I'm at work is the fact that my rolling office chair's wheels rotate whenever I push it forward or backward from my desk, which can cause it to bump my computer ...
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Velocity of a satellite with a polar orbit with respect to the surface of the earth
Let's say I'm tryng to derive the expression for the velocity of a really low orbit satellite. Let $S$ be the frame of reference of the earth's center (in rest). Let $S'$ be the frame of an observer ...
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What happens when an impulse is applied at right angles to one end of a rod (free to move on a frictionless surface)? [duplicate]
What will be the difference if we apply this impulse at the center of the rod? Will the translatory motion be same in both the cases?
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Conceptual explanation: Finding revolutions over a given time interval
The following question from NJCTL was assigned for me as homework. It is not a heavy computational problem, but rather, a conceptual one. I reviewed the meta guide regarding these types of questions ...
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3answers
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Why does friction not accelerate a wheel?
It seems like a silly question because this defies common sense, but it appears that friction is supposed to accelerate a wheel (not attached to anything).
We can derive from Newton's laws that $\...
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1answer
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Position vector from the axis of rotation in a rotating sphere
In Fluid Mechanics textbook, I found the following example:
In the rotating sphere viscometer, a solid sphere of radius $R$ is suspended
from a wire and rotates slowly at constant angular ...
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3answers
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What happens to moment of inertia if a body is divided into 2 congruent part?
If a circular disk is cut in half, and a square plate is divided into 2 identical right angled triangle, when the axis of rotation is not changed i.e if the square plate was rotating about an axis ...
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4answers
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Does rotational kinetic energy always implies translational kinetic energy?
I always thought that whenever there's rotational kinetic energy, there's also translational (linear) kinetic energy. The opposite is not true. There can be translational kinetic energy without having ...
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Theorem of relative derivatives, Mozzi Equations and Theorem of relative motion
I am currently studying Kinematics in a Mechanics course and I am unable to find sources besides college material to help me studying what I learn in classes, probably due to my ignorance regarding ...
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Boomerang problem, can't figure out the angular acceleration? [on hold]
Here is the problem:
A boomerang is thrown with an initial linear velocity of 5 m/s at an angle of 30 degrees vertically. The initial angular velocity is $2\frac{revolutions}{s}$At its peak, it has ...
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2answers
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Intuition for formula of tangential component of acceleration in general curvillinear motion
In certain problems of plane motion, the position of the particle P is
defined by its polar coordinates $r$ and $\theta$. It is then convenient to resolve the velocity and acceleration of the particle ...
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A question on the rotational motion of a metal drinking cup
When I rotate a metal drinking cup slowly it rotates normally. However, when I rotated the cup with a much greater speed, the cup's body started to rise and was rotating with a small portion of its ...
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0answers
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How to change rotating frames?
This problem is related to rotating reference frames. $p$ is a precessing frame or turning table that rotates at $\mathbf{\omega_p}$, and $m$ is a container that spins on the top of the turning table ...
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1answer
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Is angular momentum conserved radially in a rotating body?
How does the conservation of angular momentum work radially with respect to a rotating body?
For example, if a rotating body, such as a spinning top, were to lose an outer layer or shell, would it ...
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1answer
50 views
When a body completes one revolution around a circular path will its acceleration be 0?
When a body is moving in a circular motion the acceleration keeps changing, will it be zero when it comes back to the same point it started from(will the average acceleration be 0?)
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Adjust platform level by moving three jacks it is standing on
A platform has 3 jacks which can be used to adjust its level. Current platform level is determined by the angle between its normal vector and z-axis. How can the non-zero level be adjusted to the ...
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What is the angular acceleration for a mass on a trajectory with decreasing radius?
Consider the following situation: A mass in swinging on a regular pendulum on a rope of constant length $r$. Here, the torque is only given by the tangential component of gravity $M=-gsin\theta$, ...
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1answer
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What does the notation of the subscript behind the brackets in the differential mean?
From "Theoretical Mechanics of Particles and Continua" by A. Fetter and J. Walecka.
As emphasized in the preceding section, the general expression $(7.11)$ can be applied to the coordinate vector $\...
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Forces on a Rotating Rigid Body
This question has been puzzling me for some days now and I thought I might ask you guys for some help.
Say that we have a rigid body (like a rod) that is in a vacuum in space. Furthermore, say that ...
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Angular velocity of rigidly rotating orbit in 3D
Consider a circle in 3-dimensional space. On this circular orbit, a rigid bead moves, thus changing its angle $\phi$ with a reference radius on the circle.
The intrinsic angular velocity is given by ...
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1answer
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Derivation for angular acceleration from quaternion profile
Given a profile of unit quaternions $q(t)$ that represents the orientation of a body over time, I like to get the angular acceleration $\dot \omega (t)$.
I tried to find a formula myself, but I get ...
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2answers
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Angular velocity of a body observed from a frame of reference fixed on the body
I have a body and the reference frames, one is the inertial reference frame O-xyz, the other is a non inertial reference frame O'-x'y'z' fixed on the body.
The angular velocity vector of the body ...
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How does changing the moment of inertia of an object being swung by a human affect the kinetic energy?
If a human swings a baseball bat with moment of inertia $I$ at velocity $\omega$, as hard as he/she can the swing has a given kinetic energy. If you increase $I$, then the human will not be able to ...
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1answer
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Collision of rotating sticks
Q: Two identical uniform sticks are rotating about their stationary centers with equal angular speeds. The vertical stick is slowly raised until its top end collides with the center of the horizontal ...
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Screw Axis and other rotational axes
I have been trying to close the loop on the concept of instantaneous axis of rotation ISA, also called screw axis. I see how this axis, both in 2D and 3D, is a unique axis (locus of points having the ...
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2answers
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Torque, Angular Acceleration and Linear Acceleration
We know that we torque is applied, it cause an angular acceleration in the rotating body similar to what a force does to a body moving on a straight line.
But my question is, Does Torque affect the ...
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4answers
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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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3answers
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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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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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1answer
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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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3answers
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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
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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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1answer
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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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3answers
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A question on rigid body dynamics [closed]
What is the intuition for angular momentum of a point mass relative to a inertial point?
My next query is when a car moves about a circular turn then static friction operates and it provides the ...
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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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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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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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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 ...
