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

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DC Motor Torque Constant

I am very new to DC motors and to stackexchange. Please correct me if anything I said does not make sense. For DC motors, the equation looks like this: $P = \tau\dot{\theta}$ where $P$ is power, ...
2
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1answer
309 views

Transform torque from Euler angles to infinitesimal Cartesian rotations

For a certain pair of rigid bodies, I have the gradient of energy in terms of Euler angles. I want to transform this gradient to the gradient of energy in terms of rotations about the $x, y, z$ axes ...
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2answers
3k views

What causes precession or nutation in a spinning object?

What causes precession in a spinning object? What causes nutation in a spinning object? What causes a top, gyroscope, and the earth to wobble? Just because it's a simple question, I'm not ...
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5answers
583 views

Forces acting on a point mass in a spinning rigid body

I have learned that all spinning objects will continue spinning even if no force is acting on it, and the tendency to do so is called moment of inertia. But I wonder about the fact that a single point ...
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2answers
1k views

Which is the axis of rotation?

This should be simple, but it keeps bothering me. If a rigid body has no fixed axis, and a torque (defined relative to a point $A$) is applied, it will rotate around $A$. But often I can also ...
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0answers
895 views

Neglecting friction on a pulley?

So, this is how the problem looks: http://www.aplusphysics.com/courses/honors/dynamics/images/Atwood%20Problem.png Plus, the pulley is suspended on a cord at its center and hanging from the ceiling. ...
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0answers
55 views

Fading transition and rotation of and object in 2D

I'm looking for sources about I guess dynamics subject. The model I'd like to solve is reduced to a question of: How does a force applied on a certain point of an object results in both fading ...
2
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2answers
255 views

Approximating Rolling/Sliding in 2D Shape

I'm trying to find more information on how a 2D shape (could be defined by a function, such as ellipse, or by a polygon) will roll across a surface. The shape could be nearly circular or quite ...
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1answer
657 views

Non-commutative property of rotation

Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
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3answers
932 views

Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram. ...
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4answers
6k views

What determines the direction of precession of a gyroscope?

I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope. However, the direction, either clockwise or counterclockwise, of this ...
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1answer
528 views

Rod slipping against block due to gravity? [closed]

A uniform rod of mass $m$ and length $l$ is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a ...
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5answers
2k views

What causes the back of a bike to lift when the front brake is applied?

What causes the back of a bike to lift when the front brake is applied? (Like in an endo.) Also, if I were to replicate this effect with a wood block with wheels that crashes against a wall (only the ...
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1answer
146 views

What happens at the end of Coriolis Deflection

Consider we launch a cannonball due south from a point at 45 degrees latitude in the Northern Hemisphere (e.g the point defined with the co-ordinate system on this diagram). The cannonball travels for ...
2
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1answer
3k views

Why is an electric motor more efficient at higher loads?

My question is driven by the plot below. We see that acceptable operating range of a motor is between 50-100% of the rated load. Below 40% or so the efficiency of the motor drops off dramatically. ...
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3answers
293 views

Why is $F = mg - T$ in this case?

The situation is as follows: I am told that $F_{net} = mg - T$ in this case, but doesn't that not take into account that $T$ isn't applied to the center of mass? Newton's second law is defined for ...
2
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1answer
231 views

Appearing To Reverse Object's Rotation

Can it be done, and if so, how does one you explain mathematically the ability to cause a rotating object to appear to change the direction of rotation? I believe it has something to do with angular ...
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2answers
579 views

Ice skater increase of energy

This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero ...
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1answer
1k views

Kinetic Energy And Rotational Motion

The problem is, "A metal can containing condensed mushroom soup has mass 220 g, height 11.0 cm and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at ...
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4answers
3k views

Which direction will the yoyo move?

This question has been around the net for a while, and I haven't seen a good explanation for it: A yo-yo is initially at rest on a horizontal surface. A string is pulled in the direction shown in ...
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1answer
1k views

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
537 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
613 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
387 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
1k 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
10k 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
312 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
65 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 ...
3
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1answer
294 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 $115.2 rad/s$, ...
4
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1answer
217 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
463 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
516 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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3answers
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
528 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
185 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
313 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
1k 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
621 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
208 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
325 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
309 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 ...
7
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1answer
704 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
6k 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
277 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 ...