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

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71 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
68 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
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1answer
191 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
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1answer
133 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 ...
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3answers
2k 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 ...
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3answers
261 views

Ideally speaking, will a rolling disk with no slipping come to a stop because of friction from the ground?

Consider a rotating disk on a horizontal plane with static friction. The contact point of the disk with the plane has null instantaneous velocity. Assuming the center of the disk has fixed $v_0$ ...
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1answer
948 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
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1answer
419 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
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1answer
145 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
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1answer
148 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
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2answers
315 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 ...
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2answers
205 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
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1answer
359 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
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1answer
244 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
1answer
460 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
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2answers
278 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
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1answer
739 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
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1answer
406 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
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2answers
44 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
2
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0answers
66 views

Difference of the O(N) Non-linear Sigma model and SO(N) Non-linearSigma model

The Hamiltonian \begin{equation} H=J\sum_{i,j}\vec{n}_i\cdot\vec{n}_j \end{equation} is invariant under a global rotation $\vec{n}_i\rightarrow R\vec{n}_i$, where $\vec{n}$ is a $N$ component rotor ...
2
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1answer
144 views

Sum of forces with liquid in rotation

It's not homework (I'm teacher). I would like to compute sum of forces on this study : The shape is symmetrical like that I'm sure the center of gravity is in the center of the shape. I compute ...
2
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1answer
140 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 ...
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3answers
87 views

Golf: spin direction resulting from striking out of the toe

If a golf club strikes the ball out of the centre of the club face with the club path on the target line through impact, and the face square to target, the ball will move towards the target with no ...
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0answers
40 views

Computing Latitude Given Quiescent Gyroscope Data

Suppose I place a gyroscope in a theoretically perfectly quiescent, closed room. Let its output be given as a vector ${\bf v} = (v_x, v_y, v_z)$ indicating rate of rotation around three orthogonal ...
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2answers
223 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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0answers
497 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
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 ...
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0answers
236 views

Why do control moment gyroscopes exhibit “torque amplification”?

There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
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0answers
261 views

Levitation rotation speed involving laser acceleration, pyrolytic graphite and a vacuum

The experment would involve a small NIB magnet levitating between or on the diamagnetic material pyrolytic graphite, unlike other forms of levitation this doesn't require power to run such as ...
2
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3answers
217 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 ...
2
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3answers
421 views

Newton's Second Law Equivalent in rotational dynamics

The law that $$\frac{d\vec{L}}{dt}= \vec{T}$$ where $\vec{T}$ is torque about a frame's origin $o$ and $\vec{L}$ is the angular momentum about that origin $o$. Can this law be ultimately (always?) ...
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3answers
523 views

Maximum angular velocity to stop in one rotation with a known torque

I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that ...
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1answer
84 views

Feynman Lectures: Trigonometry Error in Rotational Dynamics?

I'm reading through Vol. 1 Chaper 18, and Feynman says that in the system: (See here for a higher resolution copy - can't embed SVGs), the length of $PQ$ is equal to $r\Delta\theta$: If $OP$ is ...
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1answer
531 views

Why is velocity of outermost point on a rotating wheel double the velocity of centre of mass?

'In the answers to one of the questions based on rotation of a disc in my physics book the answer includes the statement 'As we know that the velocity of outermost point on a rotating disc is double ...
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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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3answers
4k views

Factors affecting torque and RPM of a motor

I'm not a physics guy, not even basic concept of a DC motor is easy for me. My question is, how these parts of a motor affects it's RPM and Torque? I had my research a while ago so I filled out some, ...
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2answers
1k views

Will a boiled egg or a raw egg stop rolling first?

If we roll a normal egg and a boiled egg at the same time on a floor 1) with friction 2) without friction which one will come to stop first (if they will stop at all) and why? Can anyone tell ...
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2answers
69 views

If a ball spinning on a rod hits another ball, what is conserved linear or angular momentum?

Suppose a 1-kg ball A is fixed to a spoke 0.2 m long, which is attached to an axle so that the ball can rotate (v=10m/s, KE=50J, $\omega$=50 rps, L=2, p=0) Now, there is a second ball B (m=1kg), ...
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1answer
279 views

What is the friction between cylinder and wall (ground)?

A hollow cylinder (radius $R$) is rolling against the wall at angular speed $\omega$. The coefficient of friction between the cylinder and the wall(ground) is $\mu$. After how many rotations the ...
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1answer
749 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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2answers
853 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
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
28 views

Gravitational Potential Energy to Kinetic Energy

When a yo-yo is released from a height $h$, the gravitational potential energy is converted to kinetic energy. However, the yo-yo obviously has less acceleration than $g$, $9.8\frac{m}{s}$. This means ...
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1answer
480 views

Moment of Inertia and Rotational Dynamics? [closed]

I'm having problems with the intuition behind the Parallel axis theorem and the Perpendicular axis theorem. I'm self studying Mechanics for the British Curriculum but, the book I've is missing the ...
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1answer
1k views

Is squared motor gearbox ratio proportional to inertia ratio?

I read an interesting article http://m.machinedesign.com/news/motor-sizing-made-easy It is very interesting, but I can not follow the 2nd last paragraph. I don't understand why it is true. ...
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2answers
368 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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3answers
1k 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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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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1answer
45 views

A pretty dumb question on observation

Very often I have seen, that a bicyclist can balance himself better, while in motion, than he can while at rest(with his legs on the paddles of the bicycle). Now, I know that objects, say, a disc ...
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3answers
55 views

Uniform Circular Motion and Centripetal Acceleration

In introductory physics books (or at least mine) it limits the equation $a_c=v^2/r$ to the situation where the speed around the circular path is constant. It enforces the idea that the speed is ...