Questions tagged [rotational-dynamics]
A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.
4,179
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Spinning astronauts - can they tell which one is spinning?
If there are two astronauts facing each other along a common axis that goes through both of their centres of gravity, and one is spinning about that axis, which one is stationary and which one is ...
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Cartesian equation of a moving rod of shape $ y = f(x)= 10\sqrt x$ that passes rigidly through a fixed ring located at a point $P= (a, f(a))$
Note : here I use the square root function as an arbitrary example of a curve moving rgidly through a fixed ring; my final goal would be to do the same thing with a closed curve such as an ellipse.
A ...
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1
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123
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What are the details that link an "inertia tensor" of a rigid body at a given point with the mathematical definition of a tensor?
I know how to operate with the matrix representation of an inertia tensor, understand how it changes with respect to basis transformations, but I'm having a hard time framing the concept of the ...
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4
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Can someone please explain Gyroscopic precession?
So I watched this video
It is a fairly popular one by veritasium, and one that confused me. I was wondering if someone can cover the physics behind this in a intutitive and easy to understand manner. ...
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1
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Uniform rod tipping over the floor
That's an exercise from Thorton's Classical Dynamics textbook.
Basically, as stated, a uniform rod of lenght $b$ tips over to the floor, being initially stood vertically upright on the same floor. The ...
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1
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583
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Gyroscopic bicycle wheel - forces on the wheel only
This is a standard problem in university physics, which I studied at university in depth. With higher concepts like angular momentum, it is fairly straightforward to explain the motion.
However, one ...
2
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0
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34
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Find resonance for vibration motor [closed]
I have a motor that spins with a certain RPM (let's consider it constant: r). I attach a weight of mass m on a (weightless) ...
2
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1
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Definition of time derivative of angular momentum (Wittenburg, "Dynamics of Multibody Systems")
In Wittenburg, "Dynamics of Multibody Systems", 2e, 2008, p.45, (3.33), the definition of time derivative of angular momentum with respect to a reference coordinate system, in its most ...
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3
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147
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Why doesn't the moment of inertia of a body equal to the moment of inertia of its centre of mass?
Moment of inertia is the summation (or integration, in case of continous bodies) of the product of the square of perpendicular distance of all individual particles in a system from the axis of ...
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4
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300
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Can angular velocity direction change in a body frame
Suppose the angular acceleration velocity of a body as measured in a fixed inertial frame (with fixed basis $\big\{\hat X_1,\hat X_2,\hat X_3\big\}$) is $\vec\omega$ with direction $\hat \omega$.
Next,...
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Does static friction affect the motion of a wheel moving at uniform velocity?
Imagine a car moving in a circular track with constant speed. I am aware that kinetic friction is responsible for the centripetal acceleration of the car. But is it right to say that the car, or more ...
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4
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Is Instantaneous axis of rotation of a disk undergoing pure rolling an inertial frame?
My teacher told that instantaneous axis of rotation of a disk in pure rolling that is point of contact of disk with ground is an non inertial frame due to radial acceleration. But I am confused that ...
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1
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209
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How to simulate a Double Pendulum with a Motor? [closed]
I'm trying to find a specific formula for a variant of the 2D double pendulum experiment, but I'm afraid my physics skills are not up to the task. I'm hoping someone here can help me :). The situation ...
3
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5
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Rope wrapped around a pole
I would like to solve this question without using conservation of angular momentum(because of some reason I'll elaborate later).
So imagine that we have a pole with radius $r$ and a ball attached to ...
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1
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Why will parts of a rigid body roll on a rough inclined plane?
If we have a rough inclined plane and a rigid body kept on it, the bottom most part of the body will rotate due to the torque produced by the frictional force. But why will any part rotate. If I am ...
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1
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Do differentials disabled by free spinning wheels?
Having a car with 4 wheels and one engine (4x4 or 4WD).
Two wheels in front (sharing one front axle using differnetial A).
Two wheels in back (sharing one back axle using differential B)
front-...
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0
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56
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Gravitational potential at large distance tensor
Prove that for a bounded body with mass disturbution $\rho (\vec{r'})$
The gravitational potential of the body can be expressed as
$\phi(\vec{r'})=-\gamma\frac{M}{r}+\frac{3\gamma}{2r^5}r_ir_j(I_{ij}-\...
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1
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Are the velocities of a falling rolling coin/wheel parallel?
Can someone confirm that a rolling coin that is falling will, at any instant, only have horizontal velocity directions that are parallel (those velocities being horizontal component velocities)?
It is ...
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1
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I'm trying to prove a formula regarding the total displacement due to the Coriolis effect of a bullet shot upwards [closed]
So my textbook gave me this formula
$$\frac{4v^3\Omega\cos{\varphi}}{3g^2}$$
where $v$ is the velocity of the bullet, $\Omega$ is the angular velocity of the Earth, $\varphi$ is the latitude, and $g$ ...
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2
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Uniqueness of Mass Moment of Inertia tensor
I was curious to know if there can exist two different objects (shape and/or mass distribution) that can have the same inertia tensor.
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Why is it easier to turn the front wheels of a car (without power steering) when it's moving than when it's stationary?
Why is it easier to turn the front wheels of a car (without power steering) when it's moving than when it's stationary?
How is this explained intuitively?
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Why does a rigid body sometimes have translational motion and sometimes rotational motion? [duplicate]
If apply some force on a pencil, it rolls and moves in a straight line but if apply some force on its edges or somewhere from the centre, it rotates by some angle. Can you please explain why does this ...
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1
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Confusion about conservation of angular momentum [closed]
A uniform rod of length l is slightly disturbed from its vertical position. Find the angular velocity of the rod just after if hits the step. (Friction is sufficient everywhere to prevent slipping)
I ...
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0
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How long for a spinning cylinder in space to stop spinning?
Suppose we spin a solid cylinder of inertia $J$ and mass $m$ to a speed of $n$ rpm. Assuming it is in close earth orbit, about the same distance as ISS, how long would it take to lose all its angular ...
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3
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Why does an extension cause my impact gun to have less torque?
I have an impact gun that I can mount an extension onto. It appears the longer the extension, the less torque the impact gun delivers ? Does this make any sense , or am I just imagining things
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Reference request - book on Euclidean space and rigid body kinematics
Ideally, I'd like a comprehensive book that encompasses both subjects: it builds the notion of "space" as related to our physical world (no relativity, though) from the ground up, giving it ...
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3
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144
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Potential at a point on Earth due to orbital motion and the Moon
In "Physics of the Earth" by Frank Stacey and Paul Davis, they approximate the height of the tides on page 103.
They assume the Earth is perfectly spherical, covered in a uniform layer of ...
2
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2
answers
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How does this spool have an angular acceleration opposite to its acceleration?
Consider this spool. It rests on a rough horizontal force. The green lines are the ground, and a line parallel to the ground. The spool is pulled without sliding by the thread (with tension T), with ...
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1
answer
134
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Moment of inertia of irregular object
How could you use a torsional pendulum to determine the rotational inertia of any object that could be mounted on the Rotary Motion Sensor?`
Note: The Vernier Rotary Motion Sensor is a bidirectional ...
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3
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341
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Two gears and the speed of light [duplicate]
Say I have two gears, with a 2:1 gear ratio. The larger gear is spinning at almost the speed of light,so what would happen to the smaller gear since it cannot move faster than the speed of light?
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3
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Integration approach for calculating the moment of inertia of a square "loop"
I must confess, most of the time when I was calculating moments of inertia I was using tables and the parallel axis theorem. Now I'm trying to compute the moment of inertia by integration.
The problem ...
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How to calculate the reaction force of an object that has just flung out from an accelerating circular motion? [duplicate]
If I am an astronaut floating in space and swirling the object with a string in my hand and then releasing it at 90 degrees relative to my front position, is my assumption correct that I would get a ...
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3
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Does the earth’s rotational angular velocity change?
This is what is written in The Feynman Lectures on Physics, Vol. 1 (ch.5)
We now believe that, for various reasons, some days are longer than others, some days are shorter, and on the average the ...
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1
answer
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Experimentally determine the Moment of Inertia of a complex (mathematically indescribable) object
I'm a high schooler that's trying to design a robot for a physics project. The robot is a catapult; it will calculate a trajectory and shoot at a certain speed and angle using a large motor. I'm using ...
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2
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62
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Does a person in relativistic circular orbit have the same age as a stationary person at the centre? [duplicate]
Consider a circular orbit whereby a spaceship travels around near the speed of light.
Say the radius of this orbit is such that the angular velocity is low.
An observer is placed at the center of the ...
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1
answer
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Work done by an eccentric force on a rigid body
I am hoping someone can explain in simple terms where I might be going wrong in my logic below.
We have a thin rigid rod (see diagram A) where a couple is acting and rotates the rod about its COM by ...
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5
answers
842
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Uniform circular motion in vertical plane: Free body diagram confusion
I'm considering the free body diagram for an object attached to a rigid rod undergoing uniform circular motion in a vertical plane where the net force acting on the object must always be acting ...
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2
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303
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Centripetal Force Acting on a Belt and Pulley System [closed]
Just a warning: I am an A Level student looking for a simple but thorough explanation. I am happy to be introduced to new ideas, but a sesquipedalian answer with formulae that aren't derived will only ...
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1
answer
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What is the maximum height a pendulum can reach? [closed]
I've been trying to solve this problem:
The sphere of mass 𝑚 of a pendulum of length 𝐿 is initially held
vertically. When a wind blows with a constant force 𝐹
non-conservative, show that if the ...
0
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3
answers
835
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Rotating Rod in Special Relativity
Statement of the Problem
In frame $F'$ with co-ordinates $(t',x',y',z')$, a straight rod rotates in the $x',y'$ plane with angular velocity $\omega ′$ about one of its ends. The fixed end is located ...
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3
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Does gravity cause the Earth's equatorial bulge?
The way I understand centrifugal force, I don't see how Earth's daily rotation alone would cause equatorial bulges to form. The usual explanation is that the centrifugal force increases with distance ...
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2
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What force accounts for Earth's equatorial bulge in an inertial frame of reference?
I am confused as to how Earth's centrifugal effects from its daily spin can be explained from an inertial frame of reference relative to the distant stars. The usual explanation is that the ...
2
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2
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If one "fell" from the center of a spinning space station, which was creating "gravity" by using centripetal force, what forces would one feel?
Let's imagine a grand hamster wheel in space. The wheel is very large and is constructed of the same reasonably inelastic material. It has three main features: The first is a solid disk rotating at ...
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Rigid body doing rotation [duplicate]
Is it possible that a rigid body is rotating but net torque about any point in the body is $0$? The reason behind asking this is if we apply two unequal like parallel forces at two ends of a uniform ...
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5
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740
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Why static friction is necessary for pure rolling instead of kinetic friction?
Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity $v$ and zero angular velocity. the kinetic friction would be applied between the ...
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2
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Role of static friction in rolling
I am confused as to how does static friction (analytically) causes rolling motion.
As far as i understand
For causing a rigid body to rotate about its centre of mass a torque must displace angularly, ...
4
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3
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During a turn, do the rear wheels necessarily trace out the same arcs as the front wheels?
When a vehicle makes a turn, the two front wheels trace out two arcs as shown in the figure below. The wheel facing towards the inside of the turn has a steering angle that is greater than that of the ...
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2
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What are the steps to the approximation for this falling pendulum problem?
I am trying to understand the math here.
How long would it take for an upright rigid body to fall to the ground?
But I am lacking in some basic mathematical concept/techniques.
In several answers, an ...
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1
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Potential Energy of 'Triple Spring Mass System'
Given the following system, I am trying to find the potential energy and equations of motion.
$\hspace{70mm}$
What I got is
$$\Pi = \frac{1}{2}(c_1(\varphi_2r_2-\varphi_1r_1)^2 + c_2(\varphi_2r_2-\...
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4
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How long would it take for an upright rigid body to fall to the ground?
Let's suppose there is a straight rigid bar with height $h$ and center of mass at the middle of height $h/2$. Now if the bar is vertically upright from ground, how long will it take to fall on the ...