Questions tagged [rotational-kinematics]

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

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40 views

How to calculate torque required to rotate a rectangular prism about its center? [closed]

I'm trying to buy a motor, but first need to find out how much torque I need. I've been struggling with this one, and any advice/help would be greatly appreciated! The motor/motor shaft (blue) will be ...
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Kinetic energy of rigid bodies about the center of mass

Suppose, we have some rigid body, that is rotating about some pivot. In this case, we can easily find the kinetic energy, by choosing a random point $P$ on the body. The kinetic energy of the body ( ...
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Torque of a rolling cylinder

I would like to ask the associated net torque equation for this diagram. Since the tension force is directed counterclockwise, my equation for the torque was However, the solution to the problem ...
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28 views

Maximum theoretical displacement from a ruler catapult

I am considering giving my students the following problem: Assume we have a ball placed upon a ruler, residing on a table. Now we drop another ball from an height $h$ onto the edge of the ruler. If $...
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What is the relationship between the number of turns of an unwinding pendulum and its radius of motion?

For a pendulum wound around a vertical pole and let go, the largest horizontal distance between the pendulum bob and the pole is r. As the number of times the pendulum is wound around the pole ...
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Kinetics\Biomechanics of throwing a basketball (Elbowjoint)

I'm trying to make a simulation of a person throwing a basketball. My goal is to have at least a shoulder and elbow joint which I can assign with various torques over time to create a motion. When ...
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1answer
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Resolving angular components in 2D Circular rigid body collision response

I am trying to make a simple 2D physics engine with circles and capsules. So far, I have been able to resolve the velocities of circular bodies after a collision, but I wish to create events like a ...
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2answers
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Can a particle make a turn in space without accelerating? Does the size of the turn it makes, make a difference?

Is it possible for a particle to have angular velocity but no angular acceleration? Even if the angular velocity does not change, does there always need to be a centripetal / centrifugal acceleration ...
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Angular acceleration related to a time dependent rotation matrix $R(t)$

Let the orientation of a coordinate frame $\{b\}$ w.r.t. a static coordinate frame $\{a\}$ be expressed by a rotation matrix $R_{ab}\in SO(3)$ whose columns represent the coordinates of the unitary ...
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Physics of "Mad Tea Party"

Let's say you have a body rotating about its centre of mass in a rotating frame. But the centre of mass of the body does not coincide with the rotation axis of the rotating frame. We can often see ...
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1answer
327 views

What percentage of the universe's energy is rotational kinetic energy?

Obviously there is constant exchange between different forms of energy, so presumably only an average could be estimated, assuming it is not an ill-posed question. Also, even if a fairly precise ...
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Why is the angular speed at the axis of rotation of a rotating disc equal to the angular speed at any other point on the disc?

I was just reviewing classical mechanics problems on Khan Academy and got the following question: I knew that the angular speeds at points II, III, and IV must be equal, but I'm not sure how you'd ...
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Does a cornering wheel turn (change the direction it travels) at its contact point or some other location?

According to vehicle dynamics, there appears to be two different ways a wheel travels a curved path. I don't think this requires an expert in vehicle dynamics because it is a simple physics problem of ...
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67 views

Why does the angular velocity use $r$ instead of $R$?

I am calculating final velocity of a Maxwell wheel rotating and translating down due to gravity with energy. I split the kinetic energy into translational and rotational kinetic energy. I am little ...
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Are Newton's Laws applicable to torque too?

Since Torque is $Fd$ where $F$ is force, $d$ is perpendicular distance between line of action of force and axis of rotation, will Newtons Laws be applicable to torque too? For e.g., if a force od $5N$ ...
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How do you determine these coefficients experimentally?

So in our lab today my friend and I had to examine the time it takes for cylinders to roll down an incline. We managed to find an ansatz on the following form after some work: $$ t = c(c_1 + x^{c_2})^{...
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1answer
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Angular velocity of pinned rod [closed]

Below is a problem I'm not really sure If I'm doing it right... As shown in the figure, two rods $PQ$ and $QR$, pinned at $Q$ and rod $QR$ is hinged at $R$. $P$ moves with a velocity $v_0$ and ...
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Kinematics of a 3-wheeled omnidirectional robot

Consider a 3-wheeled, omnidirectional robot (also called a kiwi drive). To see what this looks like see this YouTube video. We can control the motor speeds using a microcontroller. Task: We have to ...
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How to calculate the gyroscopic inertia for this exact experiment?

This question refers to the photo below. The wheel in the middle can rotate vertically without friction. The construction around it can rotate the wheel horizontally as well, also without friction. ...
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2answers
81 views

Change of a vector in a rotating coordinate system

Goldstein 3 ed, pg 171, under" rate of change of a vector " : The author derives the relationship between the change of a vector in a stationary and rotating coordinate system. In the ...
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41 views

Forces involved in this circular motion system

As seen in the image, this system involves a small mass revolving attached to a string which is anchored with a larges mass. However, investigating this made me wonder how this system is in ...
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Angular velocity of a translating and rotating frame

I want to determine the angular velocity $^{I}w^{B}$ which is the angular velocity of frame B about the Inertial frame I. The position of P relative to O is written as: \begin{equation} r_{P/O} = r_{O'...
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What does neglect friction mean?

According to my teacher, neglect friction means to neglect the work of friction. I believe that it means that the system is frictionless. Am I wrong? The problem is specifically, "A 5 kg cylinder ...
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How to determine the direction of the tendency for a rolling object to slip?

I know that the direction of static friction in a rolling motion has been asked about before, but I am specifically asking how to determine the direction of the tendency to slide. In this picture, the ...
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86 views

Is the derivative of the magnitude of a position vector the speed? Is the integral of the speed the magnitude of a position vector?

I'm reading a book titled "Introduction to Mechanics" by Kleppner, and I came across an example: A bead moves along the spoke of a wheel at constant speed $u$ meters per second. The wheel ...
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51 views

Infinitesimal rotation vector [duplicate]

Chapter 4.8, Goldstein 3rd ed classical mechanics under infinitesimal rotations (p.166~167) ($\mathbf{B}$ is an orthogonal matrix and $\mathbf{r}$ is a position vector and $d\boldsymbol{\Omega}$ is ...
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Reaction force and normal force for falling and sliding rod

In the following picture, the blue bar represents a rod that is falling from the sky and the black line represents the ground. Hence, in the picture, the moment of the impact is shown. We assume the ...
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4answers
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How do I find the rotation axis that maximises the angular momentum for a set of discrete points and velocities?

I have a set of independent particles (we can assume with equal mass), distributed pseudo-randomly in 3D space, each with its own individual velocity. What is the process by which I could determine ...
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Rotation matrix and rotation of coordinate system

If we change the orientation of a coordinate system as shown above, (the standard eluer angles , $x_1y_1z_1$ the initial configuration and $x_by _b z_b$ the final one), then the formula for the ...
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1answer
39 views

Can a torque on the rim of a solid cylinder cause rolling without slipping?

I'm getting stuck on friction (heh). Here's a simplified problem from my textbook illustrating my confusion. We have a solid cylinder of mass m and radius r, lying on its side on a table, with a ...
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Velocity of a point on a rigid body, relative to the center of mass, when the entire body is in a circular orbit

Suppose I have an inertial reference frame centered around the point $O$. At a distance $\vec{R}$ from this point, we have the center of mass of a rigid body. This rigid body is revolving around the ...
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1answer
57 views

Rotating Rod and conservation of energy

The question says "A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end (Figure is attached below). The rod is released from rest in the horizontal ...
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1answer
42 views

Torque direction and interpreting whether the object is speeding up or slowing down

I have understood that the convention is that counterclockwise Torque is taken as positive and clockwise torque is taken as negative, But my textbook says "If the net torque is positive, the ...
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1answer
116 views

Doubt in the proof of Euler's rotation theorem

The question arises the way Goldstein proves Euler theorem (3rd Ed pg 156 ) which says: " In three-dimensional space, any displacement of a rigid body such that a point on the rigid body ...
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2answers
138 views

Is it possible in principle, to analyze problems in rotational mechanics using force and mass, instead of torque and the moment of inertia?

Suppose we are studying the case of uniform circular motion. The analysis of such motion is usually done using Newton's second law as $ma=m v^2/r$. Even when the motion isn't purely circular, like the ...
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How long would it take for down becoming the opposite on earth?

Sorry if the question is unclear, I will try to explain it better. Let's say that I am standing still somewhere on the planet and I say while pointing at my feet :"Down is this way", how ...
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Reasons for using Angular momentum, Torque and Moment of inertia to describe rotational motion

In order to describe rotational motion, we usually ditch the familiar concepts of force, linear momentum and mass, and use instead their moments to describe the motion. Is it just because it makes our ...
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1answer
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Tangential acceleration of a two-dimensional rotating mass point [closed]

An object moves on the trajectory $$\vec{r}(t)=c\cdot\big(\theta t,\sin{(\theta t)}\big).$$ I know how to calculate the vector of acceleration (second derivative of $\vec{r}$). $$\vec{a}(t)=c\cdot\big(...
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2answers
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Does the centrifugal force of a rotating object acts at this same rotating object?

when rotating an object by a string a centripetal force from the string will act at the object towards the center and by Newton's 3rd law an opposite force will act at the string by the object . Then ...
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Determining the minimum amount of torque to make wheels start rolling

Context: I am building a cart with mass m (including the cart and the payload) that has 4 wheels. The 2 back wheels will be driven by motors. I am trying to determine the minimum amount of torque ...
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3answers
71 views

Why is the direction of friction different in case of rolling on plane surface and on an inclined plane?

I was studying the rolling of spherical objects on plane surfaces and inclined planes. I had doubts about the direction of friction in both cases. Case 1- In the first case i.e. rolling on the plane ...
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1answer
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Tangential velocity - Spherical coordinates

In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as: $$V_x = -\omega_z R \sin\...
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Elliptic motion [closed]

I'm given the following motion: $$x(t)=A\cos(\omega t)\\y(t)=B\sin(\omega t)$$ I'm asked to describe what kind of motion it is and other things. The thing that puzzles me is that my first approach was ...
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Vector cross product formula without a second term (Spiegel, Theoretical Mechanics)

In Spiegel's Outline Of Theoretical Mechanics (more precisely in the Moving Coordinate Systems chapter, § "Derivative Operators") I find (both in the 1968 and the 1977 edition) the following ...
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The impact of mass distribution on time taken for a cylinder to roll down a ramp

I am carrying out an experiment to test out the impact of mass distribution on time taken for a cylinder to roll down a ramp. I have kept the overall mass of the cylinder constant, as well as the ...
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1answer
93 views

Work done when decreasing the radius of a rotating object [closed]

This is 4.4 in Taylor's classical mechanics textbook. "A particle of mass $m$ is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a ...
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1answer
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Resultant velocity in rolling motion

Why is the resultant velocity of a particle inside a body undergoing rolling without slipping always perpendicular to the line segment connecting it and the instantaneous axis of rotation? $P_2V_2$ ...
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1answer
26 views

Finding Average Acceleration with only given angle [closed]

A car enters a curve in the road with a speed of 32 m/s and emerges from this curve 4 s later with the same speed. However, the direction of the velocity changes by 150 degrees during this time. What ...
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2answers
83 views

Does angular velocity obey vector addition?

Suppose I take a water bottle and impart two angular velocities on it simultaneously, i.e. along the axis of the bottle of the axis of the bottle itself about another axis perpendicular to it what ...
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1answer
98 views

Predicting future position given linear velocity and angular velocity at $t=0$

I'm working on predicting the path of a point in 3D space for a game; at any moment, I'll have the point's linear velocity vector $\vec v (x, y, z)$ in m/s, and angular velocity $\vec\omega$ in rads/s ...

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