# Tagged Questions

A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

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### Deducing latitude from Foucault Pendulum

Suppose I set up a Foucault pendulum and observe that it precesses at a rate of 216.528 degrees per day. While I am observing this, a total solar eclipse occurs. Where am I, and what is the date? My ...
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### Force applied off center on an object

Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. ...
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### Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
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### Why are Euler's equations of motion coupled? Physical explanation

I have a problem with one of my study questions for an oral exam: Euler’s equation of motion around the $z$ axis in two dimensions is $I_z\dot{\omega}_z = M_z$, whereas it in three dimensions is ...
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### Rotation of diatomic homonuclear molecule

I know that the rotation energy of a diatomic homonuclear molecule is $E_{Rot}=\frac{\hbar J(J+1)}{R^2 M}$. Does the axis of rotation depend on $J$? With respect to which axis does the molecule for ...
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### Angular acceleration of stone disk

I have a conceputal question regarding the following problem: A round massive stone disk with diameter $0.600 m$ has a mass of $50.0 kg$. The stone rotates at an angular velocity of $115.2 rad/s$, ...
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### Stability of a rotating ring of multiple electrons at relativistic speeds

There was a time when physicists where concerned about electron internal structure. The rotating ring model was one of the proposals to explain how a charge density could become stable against ...
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### Extracting acceleration vector from rotated aircraft

Suppose we have an aircraft with accelerometer measuring accelerations along each axis. It is mounted in a way so it is perpendicular to the plane in all axes (that should be obvious). We also have ...
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### Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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### Hamiltonian is conserved, but is not the total mechanical energy

I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
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### Rotating/Translating Disk

I was trying to understand an aspect of rotational dynamics and thought of a problem to help me learn. I'm sure this problem has been considered by countless people in the past, but I'm having some ...
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### Time period of torsion oscillation

For the oscillation of a torsion pendulum (a mechanical motion), the time period is given by $T=2\pi\sqrt{\frac{I}{C}}$ which is a result of the angular acceleration ...
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### How do the energy eigenvalues of rotational degrees of freedom in statistical mechanics come about?

I want to understand the hierarchy different degrees of freedom of a mechanical system. Specifically, I want to understand which subsystems equibrilate faster and why. This question comes up: Why ...
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### Elementary derivation of the motion equations for an inverted pendulum on a cart

Consider a cart of mass $M$ constrained to move on the horizontal axis. A massless rod is attached to the midpoint of the cart, having a mass $m$ on its endpoint. See wikipedia for a picture and for a ...
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### Why does a cuboid spin stably around two axes but not the third?

Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$. Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, ...
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### If a pendulum is on a rotating table, will a torque be generated?

Here is the set up. Very simple. A flat (i.e. horizontal table, there is no gravity) and rounded table that spins on its axis (through the center of the table). A spring mass system is now put on the ...
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### Can an electric motor force angular momentum not to be conserved in an isolated system?

An ice skater is in a spin, she pulls her arms in and she spins faster, she lets her arms extend outward and then she starts to slow down. She will probably weigh on a weigh scale about the same ...
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### Does a toy top weigh less when it is spinning?

I am under the understanding that a toy top will weigh less when it is spinning. The Russians made a spinning type transport back in the 70s to lessen its payload over the tundra. Is this an effective ...
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### Why do rolling disc (coin) move in circular path?

We have a coin that is rolled such that it's tilted at an small angle $\theta$. Question:: What turns around rolling disc so that it traces circular motion (spiral as it's speed decreses)? ...
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### Ideal 2D Unicycle Kinematics

A particle is connected to a massive wheel by a rigid rod. The wheel can roll without slipping on a horizontal surface. The particle is free to rotate around the centre of the wheel. I believe the ...
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### What controls whether a ball will skid or roll?

A billard ball is struck with a cue. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity $v_0$ of the ball, its radius $R$, its mass ...
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### Why do wheels appear to revolve opposite to the direction they are rotating?

When viewing cars that are driving along side of us, sometimes their wheels appear to be turning backwards even though they are traveling in the same direction as our car. Why do they look that way?
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### Direction of rotation of a celing fan

From Constellation Energy Quick energy efficiency tip: To stay cool and manage your energy at the same time, use ceiling fans to create a “wind chill” in rooms you are using. The wind chill ...
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### What is the principle behind centrifugation?

What is the principle behind centrifugation? I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite ...
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### Meaning of angular velocity in a rotating system

When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
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### Determining axis of rotation from angular speeds about axes

I think my pure-math head is messing with me on the question below: my physics and CS friends both seemed to think it was a simple computational thing, and my program says the method works, but now ...
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### Do the rings in Mass Effect's mass relays (2-axis gimbal) describe a stable rotation?

Just out of curiosity. In the game Mass Effect, devices called mass relays contain two rotating rings, one inside of the other. See http://www.youtube.com/watch?v=qPxw5QjxhIs for an example, best seen ...
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### Moment of inertia of a sector about its center point?

What is the moment of inertia of a pizza slice that has a radius r, an angle (radians) of theta, and a height of h about the center point perpendicular to the cheese plane?