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

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2
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1answer
5k 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. ...
2
votes
1answer
200 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 ...
2
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1answer
104 views

Synchronising the Earth's rotation via mass redistribution

How much material would have to be moved per year from mountain-tops to valleys in order to keep the Earth's rotation synchronised with UTC, thus removing the need for leap seconds to be periodically ...
2
votes
1answer
946 views

Lean angle of a turning bicycle

I'm asked to derive a relationship for the leaning angle of a bicycle with the following specs: Center of gravity for bike and rider is a distance $L$ above the ground when vertical, and the total ...
2
votes
3answers
818 views

The rotating movement of an asteroid

I almost all movies where you could see an animation about an asteroid, they move in a very distinct way. I don't know how to explain better, but I think what we can see in the movies is that the ...
2
votes
1answer
49 views

Spinning rubber ball with equatorial ridge

I have this rubber ball with something like a very slight equatorial ridge (sort of like Saturn's moon Iapetus) which I often spin around on my desk. I keep noticing that no matter the inclination of ...
2
votes
1answer
61 views

Cylinder inside a cylinder - moment of inertia

A homogeneous cylinder with radius a and mass m rolls in a hollow cylinder with radius R. Determine the kinetic energy of the cylinder as function of $\dot{\theta}$. I'm sorry for ...
2
votes
2answers
80 views

Does friction act on a wheel rolling at a constant speed

One of the things I've seemed to have taken for granted is that its the friction the floor exerts on a rolling wheel that prevents slip from occurring. However, I ran into something that challenges ...
2
votes
2answers
75 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
2
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1answer
127 views

Torque for a door

The question is: A door is hinged at one end and is free to rotate about a vertical axis. Does its weight cause any torque about this axis? Give reason for your answer. I think that the answer ...
2
votes
2answers
179 views

Torque, and the Law of the Lever

How fundamental is the Law of the Lever? It seems that we simply define torque as being $r \times F$, if that's the case, then torque isn't a derived quantity, is it? Something like the Law of the ...
2
votes
2answers
888 views

Coin on an turntable | Exact description of forces [closed]

Does more static friction between coin and turntable means that more it will slip off Or Just Exactly opposite of it.When I make picture of situation in my brain I am getting first statement but I ...
2
votes
1answer
103 views

Find Angular Momentum about any point

How do I find the angular momentum of a body about any point? We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and ...
2
votes
1answer
145 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
2
votes
1answer
386 views

Why is body frame angular velocity nonzero?

This question is relevant to Euler's angles and Euler's equations for a rigid body. Why aren't $\omega_1$, $\omega_2$ and $\omega_3 = 0$ in the body frame? How can we measure $\vec\omega$?
2
votes
1answer
1k views

Calculating Rotational Inertia Using Parallel Axis Theorem

I am working on the following physics problem and have run into some trouble The figure above shows particles $1$ and $2$, each of mass $m$, attached to the ends of a rigid massless rod of ...
2
votes
4answers
274 views

Is there an upper limit on the radius of a rotating wheel?

Is there an upper limit on the radius of a real wheel which is rotating at an Angular frequency of $\,\omega \,$ along its axis, such that we just require a finite amount of energy to rotate it? ...
2
votes
1answer
340 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 ...
2
votes
3answers
211 views

Effect of surface treatment on fair dice

If I have a perfectly balanced and thus fair cubic die, then polish 3 adjacent faces (so that their coefficient of friction is effectively zero) and roughen the remaining faces (so that their ...
2
votes
2answers
332 views

Why do balls in a spinning ellipsoid move to the minor axis plane?

There is a question concerning the Physics of a small child's tall that has been bothering me for some time now. I have investigated this to a small degree, but I have not been able to find a ...
2
votes
3answers
56 views

Are angular acceleration and velocity frame dependent?

Basically what I am trying to ask is if a body has an angular velocity $\omega$ or angular acceleration $\alpha$ about an axis then will it have the same angular velocity and acceleration along any ...
2
votes
1answer
98 views

Ball rolling on half-pipe

It is well-known that a ball rolling down a half-pipe where the side it starts on has enough friction for the ball to roll without slipping and on the side other to be frictionless, that the ball will ...
2
votes
1answer
83 views

Transfer between translative KE and rotational KE in a rigid body

I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering ...
2
votes
1answer
159 views

Why are the principal axes about the center of mass of a cube perpendicular to its faces?

I have calculated the moment of inertia tensor of a cube about its center of mass: $I=\dfrac{1}{6}Mb^2\{1\}$ where $\{1\}$ is the identity matrix. So the principal moments of inertia are all 1 (1 is ...
2
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2answers
383 views

Rolling of a disk and sphere

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has ...
2
votes
1answer
138 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
2
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1answer
151 views

Falling off a chair, how best to save yourself

If I consider a man sitting on an office chair that reclines backwards iff you lean backwards. What could be done to prevent hin from falling? a) raising his legs till they are parallel to ground. ...
2
votes
1answer
285 views

Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
2
votes
1answer
148 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
2
votes
1answer
631 views

Does the Magnitude of the Drag Coefficient on a Rectangular Prism vary with Rotation?

I have a question about the drag coefficient in the drag equation. Let's say I have a rectangular prism oriented such that, looking down on it, the long side is parallel to the y-axis. Moving forward ...
2
votes
1answer
184 views

Angle of rotation of an ellipsoid in a linear shear flow field

I am modeling the motion of an ellipsoid in a linear shear flow field. The ellipsoid is rotating about its shortest semi-principal axis which I have designated the $z$-axis in the body-fixed frame, ...
2
votes
1answer
219 views

Mechanics of a rolling drum

I have no clue on how to approach this. The professor only discussed centripetal acceleration and angular velocity (As in $2πr\over T$ $= ωr$). Does the acceleration along the axis of the drum act ...
2
votes
2answers
531 views

Rotating spring system: Is my intuition correct?

Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of ...
2
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2answers
325 views

Deriving $T = F\ r = I\alpha$ for a rigid body

For a single point mass : $\tau=F_{t}r=ma_tr=(m r^2)\alpha = I\alpha$ For multiple point masses bound together : $\sum \tau_i = (m_ir_i^2)\alpha = I\alpha$ But how do we go from that to $I\alpha = ...
2
votes
1answer
572 views

Optimal door opening

This is a problem that has been periodically bugging me, so I finally decided to work on it. I haven't done any physics since high school, so I'm a bit out of practice: Consider a doorway with two ...
2
votes
1answer
403 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 ...
2
votes
2answers
309 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 ...
2
votes
1answer
671 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 ...
2
votes
2answers
378 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 ...
2
votes
1answer
1k 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 ...
2
votes
1answer
506 views

Realistic projectile motion

I am working on a project involving a simulation of the motion of a projectile (in 3D) aimed at a moving target. The way projectile motion is analyzed in most introductory physics books is not ...
2
votes
1answer
921 views

Relation of angular speed of a rigid body to Euler's Angles

My Question was like this and i have realised few things and still have some doubts I have a book in which a paragraph goes like this Now, $\dot\phi$, $\dot \theta$, $\dot\psi$ are respectively ...
2
votes
0answers
39 views

Autocorrelation function corresponding to density of states with significant rotational motion

Most statistical physics textbooks (at least the ones I've found) state simply that the density of states of a system can be found as the temporal Fourier transform of the velocity autocorrelation ...
2
votes
2answers
151 views

How many hours will be in a day if the radius of Earth increases by 70 m?

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
2
votes
3answers
98 views

An object is placed on an inclined plane. Does it roll? [closed]

An object is placed on in inclined plane. There may or may not be friction, your choice. My question is, how do we figure out whether or not it rolls? For example a sphere rolls but a cube doesn't.
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0answers
85 views

Rod rotated by elastic string [closed]

A uniform rod $AB$ of length 2m and mass 1kg, has a mass of 1kg attached at $B$. It can rotate freely about a horizontal axis through $A$. The end $B$ is attached by means of a light elastic string ...
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3answers
73 views

The storage of kinetic energy in a flywhell?

I am reading a book on physics demonstrations and problems, and one of the problems deals with a flywheel which rotates at maximum angular speed. The density of the flywheel is uniform and the ...
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0answers
69 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
2
votes
1answer
81 views

How to get the linear and angular acceleration generated by a force vector field?

I am working on a physics simulation and I have to calculate the angular acceleration in degrees per seconds squared around the point on the object located relatively to the center of a vector field ...
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0answers
103 views

How to determine radius of curvature of cycloid using centripetal acceleration?

Whenever it comes to radius of curvature of complex curves like cycloid, we all take the help of calculus. But I am still in high school and not that competent with calculus, so please do not answer ...