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

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Finding Rotational Kinetic Energy Of A Clock

The problem I am working on is: Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure ...
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2answers
5k views

Tensions And Pulleys With Masses

The problem I am working on is: "A block of mass m1 = 1.80 kg and a block of mass m2 = 6.30 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m ...
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1answer
486 views

How does the resistance force on a rolling ball depend on the ball radius?

A billiard ball set gently rolling on a billiard table slows and stops, because it is decelerated by resistance forces at the contact between the ball and table. I expect the magnitude of the ...
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2answers
484 views

Setting up equations for a Rotational Kinematics system

I'm having a hard time setting up equations for the following problem: A green hoop with mass $m_h$ and radius $r_h$ m hangs from a string that goes over a blue solid disk pulley with mass $m_d$ ...
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1answer
307 views

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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2answers
907 views

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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3answers
8k views

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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1answer
303 views

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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1answer
62 views

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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1answer
224 views

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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1answer
210 views

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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2answers
438 views

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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2answers
437 views

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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2answers
2k views

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 ...
3
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1answer
479 views

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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3answers
2k views

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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1answer
182 views

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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1answer
214 views

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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1answer
999 views

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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4answers
569 views

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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1answer
196 views

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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3answers
1k views

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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4answers
1k views

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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2answers
292 views

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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1answer
283 views

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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1answer
657 views

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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3answers
5k views

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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3answers
2k views

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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2answers
1k views

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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1answer
262 views

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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3answers
483 views

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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1answer
562 views

Is this a quaternion representation of the equations of motion of General Relativity?

In The Quaternion Group and Modern Physics by P.R. Girard, the quaternion form of the general relativistic equation of motion is derived from $du'/ds = (d a / d s ) u {a_c}^* + a u ( d {a_c}^* / ...
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2answers
1k views

In a circular pendulum, where does the equation $v=\sqrt{rg\tan{\alpha}}$ come from?

In a circular pendulum the $v$ of the particle is $$v=\sqrt{gr\tan{\theta}}$$ where $r$ is the radius and $g$ is the gravity(positive sign), which is equal to ...
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1answer
108 views

Period of an Object in Periodic Motion

My attempt (if it matters): The initial period is given by $T_X = \frac{2\pi X}{v}$ for some $v$. The new period is given by $T_Y = \frac{2\pi Y}{v}$ for the same $v$. $Y = \frac{X}{2}$, so ...
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3answers
1k views

Conservation of angular momentum for a rigid body rotating about a fixed point

Picture a rigid body such as a sledge hammer. Imagine that the base of the handle is attached to a fixed point such that it can rotate but not translate. I give the hammer a good push to get it ...
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2answers
861 views

How to interpret this vertical circular motion problem?

A bucket of water is tied to a rope and swung in a vertical circle. The distance from the bucket centre to the axis of rotation is $2.08m$. Calculate the angular velocity (in $rad s^{-1}$) of ...
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1answer
400 views

What techniques can be used to analyze a rod rotating about the edge of a table?

A uniform rod of length $4x$ is rotating about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making ...
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1answer
785 views

Normal force in a compound pendulum (physical pundulum) system?

Consider a compound pendulum pivoted about a fixed horizontal axis, illustrated by the force diagram on the right: # Okay, I can't figure out where the normal force on the pendlum should point ...
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2answers
4k views

Rotational kinetic energy during vertical circular motion of a particle

Why is it not necessary to take into account rotational kinetic energy when using the Law of Conservation of Mechanical Energy to solve vertical circular motion problems? After all, the particle is ...
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2answers
377 views

What sustains a rigid body's rotation at its constant angular(rotational) speed?

Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? : Consider someone pushing a roundabout in a playground. Initially the roundabout is ...
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3answers
2k views

Centripetal force of a rotating rigid body?

Consider someone pushing a roundabout in a playground. Initially the roundabout is stationary, but when it is pushed, it rotates with increasing rotational speed. The force of the push is ...
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1answer
224 views

Relationship between the “angle of the floor” and the angular velocity in a banked turn?

Wel, imagine that you're in a carousel, and the floor is, let's say at $\theta=0$ so it's totally horizontal, if $\theta=90$ the floor would be vertically. The object put above the floordoesn't move ...
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1answer
283 views

How do I visualize the non-coaxial rotation of this device?

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass ...
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3answers
1k views

Work Done by Rockets in Orbital Motion

A weather satellite ($m_s = 4350$ kg) is in a stable circular orbit around the Earth ($m_E = 5.97 \cdot 10^{24}$ kg). It completes an orbit once every 2 and a half hours. (I'm sure about these 2 ...
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0answers
502 views

Why does a coin falls faster when it's flipping as well?

From my experiments with measuring how fast a coin falls, I have consistently measured a faster falling rate for a coin that flips as it falls. As an example, a coin dropping on its edge from height ...
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0answers
107 views

Videos of changing the orientation of an astronaut in space

Kane, Headrick and Yatteau describe in their paper "Experimental investigation of an astronaut maneuvering scheme" possible maneuvers to change the orientation in space without external torque. Is ...
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1answer
1k views

Calculation for force generated by a rotating rectangular blade

When trying to calculate the lift force generated by a simple rectangular blade, I've found the following equation: $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in which $\omega$ is the angular velocity, $L$ ...
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2answers
794 views

Moment of inertia of a coin

I have a a coin infinitely thin, rotating along the diameter. How to derive the formula for it's moment of inertia passing through the diameter. I was suggested to use the surface density and ...
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3answers
5k views

Factors affecting torque and RPM of a motor

I am not a physics guy, so not even the basic concept of a DC motor is easy for me. My question is as follows: How do these parts of a motor affect its RPM and Torque? I had my research a while ago ...
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0answers
1k views

Forces and torques about the CENTER OF MASS of a physical pendulum

I'm currently stumped by the following situation. Say we've got a rectangular physical pendulum (think ruler with a hole-punch at one end). It's trivial to analyze the motion of the pendulum with the ...