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

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3
votes
2answers
47 views

What is an intuitive explanation using forces for the equatorial bulge?

The earth is not a sphere, because it bulges at the equator. I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs. Is there (a) a ...
0
votes
1answer
39 views

If the axis of rotation is fixed, is it ok to say clockwise torque?

I know that the direction of torque is along the axis of rotation, but would it be acceptable to say, for example considering a vertical thin rod in the x-y plane with a force acting on the bottom end ...
0
votes
2answers
57 views

Inertia matrix of a rod rotating about an axis [on hold]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
1
vote
1answer
99 views

Molecular rotation - Energy levels for an asymmetric molecule

For a molecule with spherical symmetry, the energy level of rotation for quantum number $J$ is: $$E(J)=\frac{J(J+1)\hbar^2}{8\pi^{2}I}$$ "$I$" is the Moment of inertia for the molecule ...
2
votes
3answers
666 views

Force applied to wheel in pure rolling motion at contact point with road

Suppose a wheel with radius $R$ is resting on a non-inclined surface. A torque $\tau$ is applied to the wheel center. In an attempt to prevent wheel from spinning, the ground applies a static friction ...
2
votes
1answer
113 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 ...
0
votes
1answer
25 views

Coordinate System vs. Angular Properties vs. Centroid

Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., Wikipedia's Torque, ...
0
votes
1answer
75 views

Purely mechanical description of how gravity causes a gyroscope to precess

I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is ...
1
vote
2answers
62 views

Rod sliding on a frictionless surface

A uniform rod$(m,l)$ is standing vertically on a horizontal frictionless surface. Gravity is downwards and uniform. I give its upper end a little push and off it goes. I want to find the Normal ...
1
vote
1answer
23 views

Moment of inertia of a sphere

I'm looking at sample calculations of moment of inertia of a sphere here. In the first example (disc method), it has the integral as $dI = \frac{1}{2}r^2 \,dm$, while in the second example (shell ...
0
votes
0answers
30 views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
9
votes
1answer
241 views

Nuclear Magnetic Resonance (NMR) Conceptual Questions

Let $M$ be the magnetic moment of a system. Below are the Bloch equations, including the relaxation terms. $$\frac{\partial M_x}{\partial t}=({\bf M} \times \gamma {\bf H_0})_x-\frac{M_x}{T_2} $$ ...
2
votes
2answers
38 views

Describing a motion of gyroscope with gimbal

Can you tell be how to set the equations to describe the motion of this machine in movie "Contact": https://www.youtube.com/watch?v=TSaO9VGjLXc This is gyroscope with gimbal, am I right?
0
votes
0answers
97 views

Why is momentum not conserved? [closed]

A uniform free disc in rotating in a horizontal plane ($m,R,\omega$). The surface is frictionless. A point mass of $2m$ is dropped on it from a height of $5m$ vertically at distance of $\frac R ...
1
vote
0answers
55 views

Restrained double pendulum

The equations of motion of a double pendulum are well-known. Usually you'd have the them expressed in the rotations $\theta_1(t)$ and $\theta_2(t)$. There are two degrees of freedom. Now consider the ...
-2
votes
0answers
45 views

How much energy would you need to halt Earth's spin?

I was curious about the feasibility of stopping the Earth from spinning. A way to start I suppose is by getting an idea of the theoretical energy requirements.
0
votes
1answer
78 views

Contradiction regarding friction of a rolling cylinder in an inclined plane

I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient. now, $$f\leqq\upsilon N$$ Again after calculating I ...
2
votes
1answer
187 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 ...
0
votes
1answer
29 views

Torque and angular acceleration with bicycle wheel

This might be a simple problem for many of you. However, please help me understand it too. I have been looking trough a lot of materials online, and I still have the following questions, that would ...
6
votes
1answer
180 views

Disk spinning at the speed of light

Of course, I mean that the edge of the disk is traveling at the speed of light. This is a question that popped into my head a few years ago when I was learning about some basic relativity in high ...
0
votes
2answers
97 views

Is it possible to calculate how fast something will roll down a hill?

If I have a wheel, I know it's mass and diameter and the slope of a hill. Can I calculate the time it will take to get to the bottom of the hill? I am doing a project for my science fair and I sent 5 ...
1
vote
3answers
373 views

Why does a two wheeler (with out any support of stand) vehicle falls down being at rest, but not under motion?

I have always seen a two wheeler vehicle not standing without any support,it either falls down to the right or to the left,may even to some other direction.But,the same two wheeler when under ...
1
vote
1answer
65 views

Calculating the time to stop a wheel with friction [closed]

I'm trying to solve the following problem, but i have no idea how to begin. A wheel of mass $M$, radius of gyration $k$, spins smoothly on a fixed horizontal axle of radius a which passes through ...
0
votes
3answers
256 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
3
votes
2answers
46 views

Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
1
vote
2answers
18 views

Rotational Velocity and Rotational Frequency

What is the difference between rotational velocity & rotational frequency? Their units seem to be the same, and I've read that one is a 'scalar' and the other is a 'vector,' but how do they ...
4
votes
4answers
499 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 ...
0
votes
0answers
23 views

An easy source to understand classical dynamics — Rigid body Rotation [duplicate]

I've been having an extremely hard time at understanding rigid body rotation. The source that I'm currently studying from has been suggested by 't Hooft on his webpage. It's by Richard Fitzpatrick. ...
1
vote
2answers
46 views

Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
1
vote
2answers
334 views

Vibration of pulley and string system

So here's the statement: A pulley of a mass $M$ is hanged using a spring (stiffness of the string being $k_1$), as shown in the image. What is the frequency of the pulley's oscillation? So that's ...
0
votes
2answers
156 views

Different directions of frictional force when objects are rolling

My textbook has two instances of rolling bodies (smooth rolling). In the first, the body is rolling on the horizontal floor with some acceleration of its centre of mass. In this case, the book says ...
1
vote
1answer
677 views

Equivalence between a charged rotating cylinder and a solenoid

Suppose we have a cylindrical shell of radius $r$ with surface charge density $\sigma$. Then we start rotating the cylinder at an angular speed $\Omega$. You can show that in this case the surface ...
1
vote
1answer
167 views

Newton's second law for rotation

Can the second law of motion for rotation, $\vec{\tau}=I \vec{\alpha}$, be used for any axis? Is there any case that acceleration $\vec{\alpha}$ is not in the direction of applied torque ...
1
vote
0answers
53 views

Having trouble with a homework problem involving rotation [closed]

This is for a past homework assignment so it's already been solved. We wrap a light, nonstretching cable around a 9.00kg solid cylinder with diameter of 34.0cm . The cylinder rotates with ...
4
votes
3answers
1k views

Direction of angular velocity

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate ...
0
votes
1answer
73 views

Derivation of Euler's equations for rigid body rotation

Sorry for using this image, but I thought this was the most convenient way of asking this question. Please zoom in. I do not understand from the line, "Now, in the body frame $T = (T_{x'}, T_{y'}, ...
2
votes
2answers
156 views

Can I make a rod in the vertical plane move with its one end on the ground in a slanting position?

Consider a rod kept vertically on the ground. I keeps the rod in a slanting position making some angle with the horizontal. Can I now move this rod along the horizontal plane by applying a force at ...
1
vote
1answer
63 views

A question about biceps and rotational equilibrium

I know that as the angle of the elbow increases, the force of the bicep increases. i.e. when angle is 180, arm is fully extended and there is 0 force from bicep. When the elbow angle is smaller there ...
0
votes
1answer
51 views

When does the angular momentum point in a different direction from the angular velocity?

I read this somewhere: $$\mathbf{L} = \tilde{\mathbf{I}}\mathbf{\omega}$$ In general, the angular momentum vector, $\mathbf{L}$, obtained from Equation above, points in a different direction to the ...
-1
votes
1answer
41 views

Linear speed of falling pencil [closed]

Find the final linear speed of pencil. Pencil would move because of gravity. Let's assume that it is balancing on the tip. We do not take friction into consideration. – Given $$d=0.15m$$ Similar ...
0
votes
3answers
81 views

Rotating reference frames

I'm trying to understand the equations that govern velocity in a rotating reference frame... \begin{equation} v_i = (\frac{dr}{dt})_r + \Omega \times r . \end{equation} I'd like to build a simple ...
4
votes
0answers
64 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
0
votes
1answer
32 views

Thrust to Weight ratio in Space with an off set CoM

With regards to this thread, Thrust center in space My question is, if the thrust to weight ratio was increased so that it was much higher than the weighted mass of the sphere (ship), would the ...
0
votes
0answers
64 views

Imagine a 50-mile tower spanning from desert floor to the Karman Line

CORRECTION: The structure weighs 1.568E15 kg.s Does the structure effect the equilibrium of earth's rotation? Would momentum from Earth's rotation apply lateral force to the structure? What else do ...
0
votes
0answers
19 views

model for flexible stick

I'm trying to model a flexible stick with a partial differential equation. I want one of the ends to be fixed and the other end to swing. Do you guys know of any good models I can use? Any ...
1
vote
2answers
67 views

Direction of friction for object that rolls with slipping

Let's say you hit a cue ball with a pool stick that causes an impulse. If the pool stick hits the ball above the ball's center of mass, is the direction of friction different than if the pool stick ...
2
votes
1answer
94 views

Lagrangian approach to spinning thread reel

I am trying to better understand Lagrangian dynamics and am struggling to complete the following question: A reel of thread of mass $m$ and radius $r$ is allowed to unwind under gravity, the upper ...
2
votes
1answer
60 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 ...
6
votes
5answers
8k views
0
votes
1answer
66 views

Why is it easier to turn a heavy hanging object?

Assume if we had a 2 tonne weight placed on ground attached with a rope that we can use to turn the object around. It will immensely hard to turn that object around by pulling the rope. However, if ...