Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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questions
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Isotopic separation and circular motion
I have read in a textbook of an high school (I not know) that exist a centrifuge with isotopic separation of the radioactive material very similar to the centrifuge for hematocrit to separate the ...
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2answers
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Angular velocity to linear velocity Modern Robotics textbook
In the second to last sentence, I have no idea how $v = (2,0)$ was calculated. Can someone derive this for me in detail, or with a picture?
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1answer
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Why the direction of the omega (angular velocity vector) is along the axis of rotation? Also for angular acceleration
I know that the direction of omega is taken along the axis of rotation but I don't understand it why it is taken?
I also know that $\mathbf v = \mathbf ω \times \mathbf r$ so, all three vectors ...
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4answers
96 views
Matrix algebra of rotations
I have heard that the basis vectors and the components of the vector transform differently keeping the vector same. Normally the Matrix notation for expressing rotation is:
$ \left(x' \quad y'\quad z'...
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3answers
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Definition of torque in the (possibly accelerating) centre of mass frame
My lecture note states that the torque in the centre of mass frame ($O^*$) of a rigid body is: $$\bf{G^*}=\sum \bf{r^* \times F}$$
where $\bf{F}$ denotes the real force that is producing the torque
...
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1answer
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How to derive the bank angle of an aircraft from its roll angle and pitch angle?
From Young (2017) (https://onlinelibrary.wiley.com/doi/book/10.1002/9781118534786) it is stated that we can define the bank angle ($\Phi$) of an aircraft as the angle between its Y body axis and the ...
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2answers
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Is the angular acceleration of a rotating body calculated about points out of axis of rotation different?
So I have probably got a major conceptual error here, But I was just confused by two problems while going through rotational dynamics.
So the first problem goes like this:
A thin uniform rod of mass $...
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2answers
81 views
In rotational motion, why $a = rα$?
The formula of torque is given by $$τ= F*r = Iα,$$ while solving some questions I came across a question of rotating pulley where these two formulas were equated to find value of $α$. How $a=rα$? a ...
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1answer
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Is it possible to find the position of spherical ball only using gyroscope raw data?
Assuming the spherical ball undergoes pure rolling and errors from gyroscope can neglected. Can I use angular velocity from gyroscope to find the position by computing rotations times its radius?
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Difference between nutation and polar motion
If you add a mass to your spinning globe or just change the mass distribution does it increase nutation or polar motion? And How do I calculate nutation? For this I take earth as an example. from what ...
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2answers
48 views
The Rotational kinetic energy [closed]
Earth has more kinetic energy than the cloud from which it was formed. Where did this energy come from?
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4answers
98 views
Angular velocity or frequency in an uniform circular motion? (for students of an high school withouts the calculus)
In an uniform circular motion, we know that the angular velocity is:
$$\omega=\frac{2\pi}{T}$$
and your measure is:
$$[\omega]=\frac{\text{rad}}{\text{s}}$$
i.e. revolutions per second (in Italian ...
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1answer
91 views
Weight lifted by cable wound on a cone
This problem is from Hounser & Hudson, Applied Mechanics: Dynamics (1959):
The answer given by the book is:
$$a = \frac{Dd \omega^2}{4 \pi h}$$
I was trying to solve it using polar coordinates (...
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2answers
40 views
If a body is lying on a frictionless surface, and we give it an impulse, will it start rotating about its center of mass?
If not, about what point will it rotate? If we want to know about what point an object will rotate in questions like these, how do we figure it out?
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0answers
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Why is a mechanical advantage less than 1 required for class 3 levers?
From what I understand, mechanical advantage is equal to the ratio of force produced to force applied, which is equal to the ratio of effort to load and effort arm length to load arm length
Therefore,...
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2answers
66 views
How to judge direction of motion?
I have this scenario
suppose a cylinder is made by joining two symmetrical cones and is given a gentle push on two rails A and B . What will be the motion of cone . Will it turn right or left
I ...
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Correct Way to Find Linear Velocities Along a Kinematic Chain
I'm following a freely available robotics course by Stanford University, which explains how to obtain linear and angular velocities along a kinematic chain.
I'm specifically concerned with the case ...
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“Kinematic” dynamics or dynamics that ape kinematic movement
This is a question related to unity's physx engine, but also a general question as well.
How do you make linear and rotational dynamics work kinematicaly? For example, I add a force to an object and ...
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Accelerometer (on a rigid-body) readings, knowing its position and attitude in an inertial frame
Good morning,
I'm trying to simulate a rigid body with some accelerometers attached to it. The aim is to simulate accelerometers readings that will be later fed into a Kalman Filter (after being added ...
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0answers
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Momentum of a body with $n$ bodies inside
So, let's say that I have a big hollow ball and I put in n small balls inside it, each with a momentum m. Then, these small balls are allowed to move freely around inside the ball. What is a bound on ...
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0answers
22 views
Rotation of cylinder inside another one. Find radius of curvature [closed]
Consider two cylinders: the first one is fixed and has a radius $R$ and another one is rotating inside the former (and has $r$: $2r > R$). Consider the moment when the small cylinder places on the ...
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0answers
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Will two masses connected by a rod sliding on a frictionless surface lift off? [closed]
Consider the following simplified model of a skater falling over: Two equal masses m are attached to opposite ends of a light, straight rod of length 2. One mass rests at (0,0) on a frictionless ...
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2answers
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Running backwards on a carousel
Let's suppose I'm on a carousel rotating with a speed $\omega$ and start running on it in the opposite direction with a speed $v$ such that $\omega r=-v$ where $r$ is the distance between me and the ...
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2answers
37 views
Would Radio Communications Between Parties Experiencing Time Differently Be Compressed/Stretched
This is a contrived and extreme example that is likely not even possible, but I'm hoping the answer will help me understand something about communications across relative time.
Imagine two individuals ...
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12answers
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Why is acceleration directed inward when an object rotates in a circle?
Somebody (in a video about physics) said that acceleration goes in if you would rotate a ball on a rope around yourself.
The other man (ex Navy SEAL, on YouTube too) said that obviously it goes out, ...
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1answer
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How the rotation is possible applied onto derivatives?
After reading kinematics of mobile robot or the rigid-body, I get something not quite undersand why it it possible.
Suppose that coordinate system $A$ is the global or the reference frame, in which a ...
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10answers
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Formula for centripetal acceleration: simple proof that does not use calculus?
I teach physics to 16-year-old students who do not know calculus. When I explain the formula for centripetal acceleration in circular uniform motion, I use this picture:
Here,
$$\vec{a}_{\text{av}}=\...
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3answers
66 views
Angular momentum in center of mass frame
While doing homework I seem to come across a contradiction. The problem is very simple, a ball with radius R is attached to a rope of length L. The pendulum is subject to gravity and oscillates in a ...
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3answers
2k views
Does a rotating rod have both translational and rotational kinetic energy?
I've recently learned about rotational kinetic energy and how an object can have both translational kinetic energy and rotational kinetic energy at the same time.
However, I get confused when I try to ...
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2answers
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Rotating disk time dilation relativity
Consider two persons A and B. Assume A's reference is an inertial reference. Consider B is standing on a horizontal rotating disc relative to A's frame. By SR, we can conclude that B clock should be ...
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1answer
97 views
How to simulate orbits?
I was trying to code a simulator of a solar system, but I cannot find out the orbit trajectory equation. I have simulated my orbits with perfect circles by using the $\cos \alpha$ and $\sin \alpha$, ...
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2answers
39 views
Circular motion in a cone, velocity dependence of height [closed]
I'm attempting to solve the circular motion problem below:
You spin a marble around the inside of a large funnel, such that it follows a circular path. How does the height $h$ above the bottom of the ...
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1answer
62 views
Projectile motion in vertical circular motion
Consider a particle attached to the centre of a circle via an inextensible string undergoing vertical circular motion. If the initial velocity $u$ is such that $\sqrt{2gl}<u<\sqrt{5gl}$, the ...
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1answer
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Condition for pure translational motion
Q:If we know that the acceleration vectors of all points of the rigid body are equal to each other at all points of time, can we conclude that the body is undergoing pure translational motion?
I ...
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1answer
48 views
Wheel slips and weight
With rainy season starting, I have been thinking about traction and have a question:
Question: If two identical vehicles, one of mass $m$ and the other of mass $2m$ are starting from rest with equal ...
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3answers
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Why do we add individual kinetic energy for particles of a rotating object but we don't do the same with objects in linear motion?
I'm studying Rotational Kinetic Energy of an Object and the section reads:
Each particle of mass mi in the object has kinetic energy, Ki:
$$ K_{i} = \frac{1}{2}m_{i}v_{i}^2 $$
We can sum the kinetic ...
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3answers
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Angular momentum and conservation of energy when sitting on a spinning chair [duplicate]
Usually, the spinning chair problem is one of the typical angular momentum problems. And most of them start with a person holding two dumbbells on his two hands and bringing his arms in, then by ...
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1answer
62 views
How do Roll, Pitch, and Yaw Interact?
I'm making a spaceship piloting game, and I'm trying to make the movement follow the laws of physics. The ship is able to control it's angular acceleration in pitch, yaw, and roll. The way I've ...
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3answers
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Why do rotating fidget spinners sometimes create a perception of opposite spinning?
Firstly, I apologise for asking this question as I really don't know if it's although a physicis question or not! I am sorry if that's not the case but from the very little age I(probably everyone) ...
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1answer
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When to consider rotating body as point mass?
I'm not asking you to solve this question, but here it is anyways for clarification purposes:
A rod of mass $m$ and length $2R$ can rotate about an axis passing through $O$ in vertical plane. A disc ...
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6answers
433 views
Conservation of angular momentum in rolling cones
Consider the situation shown in the figure, A cone is set rolling on a cone so there is angular momentum about the vertical and there is an instantaneous angular momentum that is consistently moving ...
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1answer
50 views
Why does merely changing point of application of force change kinetic energy?
Consider two spheres A and B of similar mass and radius kept on a smooth surface. If I give an impulse 'J' to one of them along its centre of mass axis, it would only translate and not rotate.
Its ...
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1answer
26 views
Is there a difference in terminology between velocity vs velocity of the center of mass?
I was wondering if there was a difference between velocity of the center of mass of an object vs finding the velocity of an object in general. The case I was looking at was in a ball rolling without ...
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3answers
120 views
Confused in Newton's second law for rotation
I'm a high school student and I am really confused about a point from rotational mechanics.
My confusion is as follows-
We are often taught that $\tau=dL/dt$ and $\tau=I\alpha$ are the same if the ...
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3answers
104 views
In Uniform Circular Motion, why does the normal accelaration not change the magnitude of velocity?
According to pythagorean theorem V2 should be greater then V1.But why doesn't it happen?
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1answer
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Am I understanding the concept of rotations correctly?
Consider a ball placed at distance $r$ from an origin point $O$ on a horizontal plane and remains stationary.
When the ball is viewed from a coordinate system which is rotating
anticlockwise about $O$...
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How does physics deal with perpetual motion in spins?
This is a bit a bit of a weird question. Simply put, if a body such as a planet spins, there is no internal issue (that I know of) that would cause it to eventually stop (by internal I mean that an ...
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1answer
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Does this kinematics problem involve rotational motion?
I'm given the following problem:
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the ...
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1answer
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Parallel shifting of mass while calculating moment of inertia only seems to work for linear objects
Since the moment of inertia is defined as $\int r^2 dm$ where $r$ is the distance of the mass element from the axis, one can move a mass element parallel to the axis, without changing the moment of ...
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2answers
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When a sphere is in pure rotation, will all particles in its surface have same linear speed?
Imagine this sphere to rotate about its diameter, from the centre to the point of surface if we take all of them have equal distance that is 'r(radius of the sphere)'.So same linear speed right? I ...
