All Questions
Tagged with kinematics rotational-kinematics
210 questions
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How to show angle between velocity and acceleration vector is constant in polar co-ordinates? [closed]
In polar co-ordinates we have
$\vec{r} = r\hat{r}$ and
$\vec{v} = \dot{r}\hat{r} + r\dot{\theta}\hat{\theta}$ and
$\vec{a} = (\ddot{r}-r\dot{\theta}^2)\hat{r} + 2\dot{r}\dot{\theta}\hat{\theta}$
...
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2
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182
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Question about circular motion
A particle moves along A->B with a constant acceleration in the x direction. I'm supposed to find the velocity at B
Therefore, at $\theta$, the centripetal acceleration for some $v$ at that instant = ...
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3
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Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?
Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity ...
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1
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3
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Proof of Centripetal Acceleration Angle $\theta$ is the same?
The book I am reading shows a proof of centripetal acceleration.
It proceeds to say that the linear velocity is always at a tangent to the radius, so the angle between $V_A$ and $V_B$ is also $\theta$...
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1
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What precisely does an angular accelerometer measure and how can one obtain an SO(3) Rotation from said measurements?
tl;dr
If one has an angular accelerometer, what is the motion that it actually measures?
If we have a perfect (i.e. noise-free, error-free, perfectly aligned, ...) 3-axis angular accelerometer, ...
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1
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1
answer
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Constraint Equations of a Sphere Rolling Inside another Sphere [closed]
Consider the motion of a sphere which is rolling (without slipping) inside another sphere.
Derive the constraint equations of the rolling condition.
Note
This is a 3D rigid body problem. In fact, ...
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5
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tangential acceleration for uniform circular motion
I understand that circular motion is defined by 2 components of acceleration, one tangential and one radial and their resultant is what causes circular motion.
I am confused though as to why it is ...
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Motion of a catapulted point mass moving freely inside a spherical bucket
I am trying to study the motion of a point mass inside the bucket of a catapult.
The catapult is shooting downward (i.e. describing a rotation of 180° from the horizontal axis) and I would like to ...
- 51
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Rotational physics of a playing card
A playing card leaves a dealers hand with some angular velocity. As the card slides across a table the friction of the table causes the rotation to slow. How is the friction coefficient between the ...
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2
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In Uniform Circular Motion, why does the normal accelaration not increase the magnitude of velocity?
This very simple question was posed by a high-school student in the class.
Consider a particle going in a uniform circular motion (uniform implies that the speed is constant). We know that there is a ...
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In circular motion is the angular velocity vector always perpendicular to centripetal acceleration?
In circular motion is the angular velocity vector always perpendicular to centripetal acceleration?
Are there any exceptions?
Why or why not?
user135951
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Driving shaft - Zero net torque yet linear acceleration exists
Imagine a scenario where we are talking about a driving shaft placed on a truck.
I am doing kinematic analysis on the subject and faced the following paradox:
The input shaft rotating speed is ...
3
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5
answers
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Radius of centripetal acceleration
Suppose you are moving in circle of radius $r$. So there should be centripetal acceleration towards the center. Now you want to decrease the radius of the circle, so someone should apply more ...
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2
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Can a system's internal forces change the system's motion?
Let say the motor makes the two rigid body rotate as a same velocity. (they rotate the opposite direction) then the Net force of the motor is 2Fsin(Theta). The acceleration of the motor is 2Fsin(theta)...
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Derivation of centripetal acceleration
While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
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2
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Momentum of a rack and pinion gear system excited by a time variant force
Background
I have a rack and pinion gear system as shown in the image below
The pinion gear is attached to a flywheel at the back.
The first state of the system, none of the gears or the flywheel ...
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3
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Why the similarity in the Equations of Motion for Rotational and Rectilinear Motion?
These are the equations of motion given constant acceleration, for first rectilinear and then rotational motion.
Rectilinear Motion:
Rotational Motion:
While the variables have changed, and the ...
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2
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Trouble with rotational kinematics
I'm having a bit of trouble with the following homework problem:
My thinking is there are only three forces acting on the laundry: the force due to centripetal acceleration, the force due to gravity, ...
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1
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1
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How fast does a long object bent at the center need to be travelling in order to boomerang?
At an angle, of course.
Standard pressure, average temperature, and calm wind.
Bonus question: Can an object that is not bent boomerang at all? If yes, how different would the equations for this ...
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Correct formulas for two wheeled robot motion
I'm trying to write a simulation of a two wheeled robot, which can be controlled by varying the speeds of his wheels, independently. However, the physics engine that I'm using can only rotate a body ...
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1
answer
987
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Force required to rotate a rod around an axis [closed]
The problem I'm trying to solve is:
How much force, momentarily applied to the rod, is required to rotate it around an axis by a given degree? Assuming there is friction applied at the axis (...
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2
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1
answer
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Find the Kinematic degrees of freedom of the following contraption
In the above mechanism it is required to find the generalized coordinates to write equation of motion of the MDOF system. I just want to ask how do we actually approach such a problem? How to identify ...
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Deriving some uniform circular motion equations
My question basically boils down to this. How do we derive these relationships.
1.)What is the relationship between radius and centripetal force? (inverse, but why?)
2.)What is the relationship ...
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1
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Time in a vertical circular motion [closed]
How can I calculate the time taken to go from one point to another, in vertical circular motion?
If we have radius, angle between 2 points, and initial velocity.
I tried to write $\frac{dv}{dt} = g \...
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What are the Kinematics of an Irregular Tripod?
It is a common maxim (at least within the Scouting community) that a triangle is the most stable shape. In practice this means structures should have three legs whenever possible, and have cross-bars ...
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1
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Velocity required for a car on a a frictionless banked surface
My textbook has clearly explained and derived a velocity that is required for a car to navigate a turn on a frictionless banked surface. I have understood it too. My doubt is about what happens when ...
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2
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Why the bob leaves the circular path when tension in the string becomes zero [duplicate]
In vertical circular motion of a bob attached with a string, we say that the bob leaves the circular path when tension in the string becomes zero.
But even when tension becomes zero there's always a ...
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1
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Angular speed and normal speed
The instantaneous speed of a point along a circular path is given by $v=\omega r$, where $$\omega = \frac{\Delta \theta}{\Delta t},$$ $s=\Delta \theta r$, and $v=s/t$.
However, isn’t the displacement ...
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Angular acceleration - radial & tangential
Since ever I knew that radial (angular acceleration) is equal to $ W^2 * R = V^2 / R $ and that the tangential depends in the situation (School physics & calculus). Recently I encountered the ...
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How Burmester's theory converts rotary motion of the crank to linear movement?
I have been studying the mechanism of Klann's Mechanical spider and there it was written that by Burmester's theory it converts rotary motion of the crank to linear movement. I tried searching but how ...
- 1,850
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1
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859
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Angular and linear displacement of a turning car
My illustration is supposed to show a simplified car (with just two wheels, where the front wheel has been rotated $-90 \text{ degrees}$). Let the car travel at constant speed. This means that the ...
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2
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2
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997
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At what point does force stop translating an object and start purely rotating it? [duplicate]
At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
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Kinematics of a differential drive robot
(I am reposting here a question I asked on stack overflow, since it actually sits right in between programming (modeling of 2D physics) and physics proper (kinematics). I think I have the physics part ...
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1
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Is this movement possible?
My friend and I were arguing over some random facebook shared video. On this video, one guy throws up a rotating stick then, while it rotates on air, he kicks through it. Is it even possible? Or is it ...
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4
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Does circular motion cause centripetal force OR does centripetal force cause circular motion?
Does circular motion cause centripetal force, or does centripetal force cause circular motion, or are they both occurring hand in hand together instantaneously?
One more question: If I project a body ...
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2
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Rolling as pure rotation
In my book the following statement was written and I didn't understand it well. Can anyone explain it in a more simple way?
Figure 11-6 suggests another way to look at the rolling motion of a ...
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1
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2k
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Does rotation increase mass?
If an object is rotated on its axis near the speed of light would its mass increase?
Normally if the object was moving (in relationship to the Earth for example) I would agree that its mass would ...
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1
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Does a tire need to slip to generate force?
Recently, I have been doing some research on racing and tire modelling. While I was doing this, I encountered many curves like those shown below.
(source: insideracingtechnology.com)
While I ...
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2
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What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?
Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
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1
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3k
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Average Velocity of a body moving in a circle with constant speed $v$ [closed]
A Body is moving with constant speed $v$ along a circle of radius $R$. Find the average velocity of the body from time $t = 0 $ to $t= \frac{R}{3V}$.
My attempt at the question:
Let distance ...
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2
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How are the angles equal?
At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal?
The only explanation present in the text is that, "both velocities are ...
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4
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Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion
The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$
However, all the proofs I've seen rely on the fact that it is ...
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2
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Find minimum distance between particles given initial position and velocity
My friend gave me a question today:
We have a point $A$. At a distance of $x_0$ from the point. There is a particle $P_1$. There is another particle, $P_2$, at $A$. $P_1$ moves with velocity $u_1$ ...
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From 3D velocity to coordinates
I want to calculate the 3D position $T_x, T_y, T_z$ of an object with respect to a coordinate system if I have the mean velocity (norm) $v$ and its 3D rotation $(\omega, \phi, \kappa)$ with respect to ...
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3
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638
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How can I compute the angular velocity of a triangle formed by three particles knowing their instantaneous positions and velocities? [closed]
I have a set of trajectories of three particles and their instantaneous velocities. I would like to compute the 3 components of the angular velocity pseudovector of the fictive triangle formed by ...
0
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1
answer
207
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Kinematics with non constant acceleration II [closed]
I'm getting crazy with this problem and I think that it's pretty simple.
An helicopter's helix is spinning at initial speed $w_0=200\ rpm$, all
of a sudden the motor stops and it decreases its ...
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1
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Total energy of a body following circular motion
I learned that when a body rotates, its total energy is,
$$energy=\left(\frac12\right)mv^2 + \left(\frac12\right)I\omega^2 $$
However, if an astronomical object is orbiting around the earth, is ...
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Motion of rigid body system in absense of work
In the absence of work on the system, is there a closed form equation for the motion of a set of constrained rigid bodies (let's say, using Revolute (ie: simple pivot) constraints)?
If the bodies are ...
- 222
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1
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Applying multiple forces to one object and calculate net movement and rotation?
I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to.
How would one go about figuring out ...
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1
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Integration on a general equation for instantaneous angular acceleration
An equation for instantaneous angular acceleration is given as:
$$
\alpha \equiv \lim_{\Delta t\to0}\frac{\Delta \omega}{\Delta t} = \frac{d\omega}{dt}
$$
The text I am reading says writing this ...
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