# Questions tagged [rotational-kinematics]

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

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### A non-intuitive kinematics problem? [closed]

Ann is sitting on the edge of a carousel that has a radius of $6\ \mathrm{m}$ and is rotating steadily. Bob is standing still on the ground at a point that is $12\ \mathrm{m}$ from the centre of the ...
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I was doing some problems in rotational mechanics. In one such problem a solid sphere was kept on an inclined plane and pure rolling was taking place. In the solutions they have applied: $$\tau = \... 2answers 47 views ### Why \omega = \sqrt{\frac{mgl_{cm}}{I_s}} for a physical pendulum? I'm trying to derive the equations of motion for the physical pendulum, and I'm confused to why \omega = \sqrt{\frac{mgl_{cm}}{I_s}}  ? Is it just a definition or can it be derived? I'm pretty sure ... 2answers 23 views ### Spinning wheel that was stopped using breaking force [closed] The wheel with radius R rotates at a frequency f_0. Applying the braking force we stop in at time t_1. What was the tangential, centripetal and overall acceleration during motion (assuming that ... 2answers 43 views ### For a simple circular motion is the tangential part of the momentum conserved in cylindrical coordinates? For simple circular motion in cartesian coordinates the angular momentum is conserved since the centripetal force has no torque to change it. Also the momentum is not conserved in any of the cartesian ... 1answer 43 views ### Two expressions of kinetic energy of rotation [closed] The moment of inertia matrix for rigid body in general case is I= \begin{bmatrix} I_{xx} & I_{xy} & I_{xz}\\ I_{xy} & I_{yy} & I_{yz}\\ I_{xz} & I_{yz} & I_{zz} \end{bmatrix} ... 0answers 8 views ### Will a rotating body which opposes some specific forces hang in air(or vacuum) [closed] **If any object that has some resistence to gravity and it is made to move fast forward, Will it have flight( drag). The actual question is, to raise the drag the object has to move forward and if ... 1answer 50 views ### What is more stable, rotational or translational motion? [closed] Let us consider a spherical body of mass m. Now my question is will rotational motion be more stable than translation motion. Also, is pure rotation more stable than pure rolling. Please give reasons,... 0answers 37 views ### Can someone help me understand this equation that finds derivative of quaternion when angular velocity is known? I found the following equation in an IEEE paper: \frac{dq}{dt} = \frac{1}{2}\text{Q}\omega where q is the quaternion that rotates a vector from the body frame to the world, q=\left[q(1), q(2), ... 1answer 33 views ### The ball-in-cylinder problem I've encountered This is going to be one of the most childish questions ever asked on this site but hear me out. Today, as I'm fiddling around with balls and toilet rolls (as one does), I found something interesting ... 0answers 15 views ### Nuclear rotation wavefunction I am a bit confused by the quantum numbers used to describe the rotation of a nucleus. In Wong's book these are J, M and K, which represent the rotational quantum number, its projection along the lab ... 2answers 36 views ### Conceptual question about calculation of moment of inertia of a rolling wheel In the problem above shouldn't the moment of inertia be \frac{1}{2}mr^2+mr^2 by the parallel axis theorem rather than \frac{1}{2}mr^2 since the instantaneous centre of rotation is the contact ... 0answers 30 views ### Ball rolling down in a tube without fricition [closed] In a tube so that its radius is R, a ball of radius r (r is smaller than R) without friction rolls from one edge to the other, only under the influence of gravity. What will be the ball speed at the ... 0answers 25 views ### How would the angular velocity change? How would the angular velocity of a rod change if the axis of rotation of changes with time. Edit: For simplicity sake assume that position of axis 'x' changes with time as x=t. 5answers 1k views ### Conservation of energy of 2 identical Rolling Disks with and without friction My physics book claims that if two identical disks moving at the same velocity travel up nearly identical hills, with the second hill not having friction, then the disk rolling up the first hill will ... 2answers 72 views ### How to explain visually and in a mathematically simple manner why the moment of inertia of a system is minimum at its center of mass? [duplicate] I've been solving different problems related with finding the moment of inertia in a set of different particles, and ojects of known rotational inertias. Let's say spheres, cylinders, rings, rods and ... 2answers 44 views ### What is the difference between circular and rotational motion? [closed] I am asking what is the difference between circular and rotational motion. Please explain. 3answers 65 views ### How does the Earth's orbit change as the Sun decreases in mass? When the sun transitions into it's red giant phase it's mass is said to decrease (An article I read quoted it to go down to 67% of its mass however the number is not important). Since the orbital ... 1answer 31 views ### Angular momentum - Equation of Motion for 2D rigid dynamics So I'm doing my best to define Equations of Motion for my 2D model of a rocket (plain cylinder). And I am stuck at the equation for deriving differential equation of the angular acceleration. I'm ... 1answer 51 views ### How do you find the Triangle Inequality from an Inertia Matrix? If you have an inertia matrix of the form$$\begin{pmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{yx} & I_{yy} & I_{yz} \\ I_{zx} & I_{zy} & I_{zz} \end{pmatrix}=I$$If the matrix ... 1answer 58 views ### Velocity of a point on the surface of a sphere rolling with slipping [closed] Here a sphere is rolling on a frictional surface but slipping takes place. Hence, the velocity of the bottom-most point is not equal to 0. Hence, v_{cm} \ne R\omega. The angular velocity of the ... 1answer 37 views ### How is angular velocity related to angles of spherical pendulum In a simple pendulum angular velocity ω is related to angle θ as$$θ = wΔt$$But what would be the relationship between the angular velocity and angles comprising a spherical pendulum described by ... 0answers 11 views ### Stable Rotation Setup for Experiments (table version) I am looking for a rotation devise like that one in this video below (from 00:40 seconds). Does anyone know where to get one, or have any idea about how to create a nice and stable rotation setup for ... 2answers 77 views ### What does \vec{\omega}\times\vec{r} equals to in circular motion? I know that \vec{v}=wr\hat{\theta} in uniform circular motion. This equation looks like a result of a cross product. Yesterday, I started to learn Basic Dynamics of Rigid Bodies. My teacher wrote \... 1answer 57 views ### Rotational Kinetic Energy of Rigid Bar Consider a rigid bar (infinitely thin and with uniform mass density) of length L with x_1(t), x_2(t) \in \mathbb{R}^3 each describing the positions of an endpoint of the bar in some fixed inertial ... 1answer 46 views ### Calculate impact force. when A beam starts to fall down with one end hinged and hits an object [closed] A beam of 10 Kg and length 12 meter starts to fall from initial vertical position with one end hinged. When Beam's center of mass is dropped 5 meter from earlier position, Beam hits an object with ... 1answer 70 views ### Is there an equation that relates angular acceleration to centripetal acceleration? Tangential to centripetal? Is there an equation that relates tangential and centripetal acceleration? I ask this question because it's been on my mind ever since I solved a problem involving the giant swing ride commonly seen ... 0answers 44 views ### Confused about choosing a rotation formalism for maximum simplicity Say we have two vectors v and w, operations of sum, difference and vector product, and normalization operations. Thus: e_x(t) = \frac{v(t)+w(t)}{\left\| v(t)+w(t)\right\| }, e_y(t) = \frac{v(t)... 5answers 130 views ### Two rotating discs with same angular momentum when brought in contact completely stop. Why is the angular momentum not conserved in this case? Two discs mounted on different thin, lightweight rods oriented through their centres are made to rotate about their axes seperately such that the angular momentum of the two about their respective ... 2answers 56 views ### How to understand Goldstein's derivation of the Infinitesimal Rotation Matrix? I can't seem to follow the chain of reasoning that leads to equation 4-100). Can anybody please help me to understand that why under infinitesimal rotation x1 transforms in the way as shown ? This ... 1answer 28 views ### Can train travelled some distances without engine? [closed] Train rolles on track without engine over 12 km how is it possible ? During engine changing , momentum is reason for rolling the train 1-2km but 12 km how? description of the incident 5answers 91 views ### Why do we use moment of inertia instead of moment of mass? I am learning Newtonian mechanics in high school. I understand that in rotational motion, the distance between center of mass and the rotational axis has also a role to play. So we find the "moment" ... 4answers 71 views ### Conservation of angular momentum and collision [closed] The problem: Consider a thin ring rolling without slipping (pure rolling) on a rough surface (means there is friction) with constant velocity v_0. The ring hits a vertical wall elastically and ... 2answers 62 views ### Factor of 2 error in angular momentum / Coriolis force calculation The problem An object is dropped from a helicopter, which is at rest relative to the Earth rotating at \Omega at height h=500\text{ m} above the ground at the equator. Without using the Coriolis ... 0answers 24 views ### Differential Drive robot non-holonomic constraint For kinematic modeling of Differential Drive mobile robot besides three differential equations they usually put non-holonomic constraint like: \begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{\phi}\end{... 1answer 36 views ### Why do we use the cross product in relative motion? The equation of motion for V_{b/a} is: V_{b/a} = \dot{r}_{b/a} = \omega \times r_{b/a} Why do we use the cross product? For some reason I am unable to gather the intuition for its use. It's the ... 1answer 37 views ### Acceleration of a Point on the Edge on a Rolling Cylinder Consider a cylinder with radius R rolling without slipping to the right. The center of mass is rolling with a velocity of v. Consider the left most point, p, on the cylinder. What is the ... 0answers 35 views ### Equation of Motion in Non-Planar Rotation I'm trying to understand the equations of motion for a rigid body that is rotating and I am a bit stuck. For a rigid body, assuming planar rotation (not necessary to be uniform), we can express the ... 1answer 26 views ### How far a sphere will move if we stick smaller sphere at different positions There is a big sphere of mass M and radius R, and a small sphere with mass m and radius r. Now smaller sphere is stuck at a certain height and angle \theta. The ball would roll to some distance. I ... 1answer 27 views ### Is the rate of rotation the same between points in a plane? Assume a body rotating around (the z-axis in) a point in a (x-y) plane. I.e. the point of rotation could be outside the body. If you measure or calculate the turn rate in any point on the plane would ... 6answers 2k views ### How can the angular velocity vector be obtained from angular displacement which is not a vector? My physics book (The Fundamentals of Physics) while explaining vector-ness of angular quantity (formally "Are Angular Quantities Vectors?") states that angular velocity and angular acceleration are ... 1answer 47 views ### Rolling restistance and angular velocity Can somebody explain why rolling resistance does not depend on the angular velocity? The drag force in liquids depends on the square of the velocity. The liquid must be deformed as well as the ... 0answers 73 views ### Components of Angular velocity Angular velocity vector is defined as, \overrightarrow{ω} = \widehat{n} \frac{d\theta}{dt} where \widehat{n} is an unit vector along the axis of rotation, and \frac{d\theta}{dt} is the angular ... 2answers 46 views ### Is the impulse given divided into linear and angular momentum? Here is the question: A uniform rod of mass m and length l is placed horizontally on a smooth horizontal surface. An impulse P is applied at one end perpendicular to the length of the rod. Find ... 1answer 89 views ### After what time, the configuration will repeat? [closed] A ball rotates at a rate r rotations per second and simultaneously revolves around a stationary point O at a rate R revolutions per second (R<r).The rotation and revolution are in the same ... 0answers 89 views ### Ball falling onto a ball at an angle [closed] Ignoring air resistance, I am attempting to create a simple model of what would happen if a ball were dropped on top of another ball on earth. The question is how to understand the interactions ... 0answers 41 views ### Centre of mass in Relativistic System We define the center of mass to be the point where, if force is applied, the system shall have linear acceleration without angular acceleration. But, think about a system of two balls, uneven in mass ... 2answers 68 views ### Relation between linear and angular velocity I'm getting really confused about when can I use$$ \vec{v} = \dot{r}\hat{r} + \omega \times r \hat{\theta}  and the following identity, which I'm not sure if it's vectorial (did I write it ...
Say I have this disk with radius $R$, mass $M$ that could rotate with angular velocity $\omega_0$ around it's CoM freely (no friction, etc). Then we have a smaller disk with radius $r$, mass $m$ that ...