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

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1answer
49 views

Is the distance involved in calculating angular momentum to an axis or a point?

I'm a high school student.I still don't really understand angular momentum and moment of inertia. I know the moment of inertia of a point mass is defined as $mr^2$. For any other shape, we integrate ...
1
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1answer
242 views

Why to use radius of gyration? [closed]

I know the definition of radius of gyration. But don't know why does it mean? What are the importances of it? Is it similiar to centre of mass?
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3answers
229 views

Why doesn't the ball have rotational energy after it leaves the ramp?

I am having trouble solving #13 from the 2010 F=MA contest: A ball of mass $M$ and radius $R$ has a moment of inertia of $I = \frac{2}{5}MR^2$. The ball is released from rest and rolls down the ...
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2answers
283 views

Is work done in rolling friction?

I am confused by rolling friction. Suppose you have a cylinder rolling which starts at rest at the top of an incline plane and begins to roll down the plane without slipping. Is work done by the ...
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0answers
39 views

How to solve this rotational mechanics problem? [duplicate]

I was doing this problem for self study in rotational dynamics: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained ...
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3answers
156 views

$F=ma$ contest problem on angular momentum [closed]

Problem #25 from the 2009 $F=ma$ contest: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all ...
3
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1answer
69 views

Changing Earth angle of revolution

As a follow-up to the two previous questions What is the scientific reason for the inclination of earth's rotation axis? and How much effort would be required to fix the Earth's rotation? ...
2
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1answer
82 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 ...
0
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1answer
158 views

Angular Velocity at different points on a rigid body [duplicate]

Why is it that Angular Velocity of a body about any point the same ? Eg: If a rod hinged at one end rotates with an angular velocity W the angular velocity about its center is also W. Also is it ...
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1answer
909 views

Unfurling a toilet paper roll in the ISS

Consider a toilet paper roll floating ISS. Can an astronaut unfurl the roll only by pulling the loose end of paper (and not holding the rest of the roll in place, for example by using his finger as an ...
3
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0answers
81 views

Protoplanetary disks, angular momentum and prograde orbits

So you've got a protoplanetary disk and you're going to gravitate yourself some planets together. The disk is made up of the usual planetary system stuff, dust and gas and whatnot, orbiting a common ...
0
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1answer
95 views

Rigid Body Dynamics - Calculating Rotation of an Object

I've looked everywhere and I can't quite find a concise answer, especially due to my limited knowledge and understanding of terminology. I found something called Rodrigues' Rotation Formula that ...
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3answers
150 views

Rotational Inertia of a Disc and Subsequent Acceleration

This is more of a conceptual problem as opposed to anything wrong with the maths! (I think/I hope! :) ) But essentially the problem states: imagine a circular flat disc of radius $R$ and of mass ...
1
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1answer
111 views

Thought Experiment: spinning ping-pong ball on International Space Station. What would Happen?

A ping-pong ball with a certain vector and rotation/spin in zero G, 1 atmosphere. If you did this experiment in a space station would the ball 'orbit in a circular fashion. or "Can you throw a ...
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2answers
463 views

What rotates a door : torque or centripetal force?

I can realize that they are different, but can't understand what actually creates a rotational motion. Rotational motion doesn't mean just moving in a circle. There must be rotation of the position ...
0
votes
1answer
69 views

Transmissibility

An extract from a school maths mechanics textbook reads: To deal with cases in which the body is not rotating freely under gravity, we need to take into account also the work done by other ...
0
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1answer
47 views

An unwinding cable problem [closed]

Suppose a light cable is wrapped around a solid cylinder with mass $M$ and radius $R$. The cylinder rotates with no friction about a stationary horizontal axis. The free end of the cable is attached ...
2
votes
1answer
79 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 ...
1
vote
1answer
107 views

Coupled wheel and rod (analytical mechanics) [closed]

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
1
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1answer
53 views

Running Euler's disk in a superfluid

I was considering the toy Euler's Disk, a video can be found here: http://www.youtube.com/watch?v=mVl2CBG_h2s I was interested in understanding the behavior of the disk particularly in vacuum and in ...
1
vote
1answer
81 views

Rotational KE in double pendulum

Why the Rotational Kinetic Energy term for the point mass of Kinetic Energy for double pendulum is not included in Lagrangian equation? \begin{align} ...
1
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2answers
75 views

Cause of rolling friction

Can you explain the cause of rolling friction? Can you tell me why, while driving a bicycle, there is less rolling friction when its tyres are fully inflated?
0
votes
1answer
33 views

When conserving angular momentum, about which point(s) should it be calculated?

In my physics problem I have a ball fired at a non fixed bar, which is moving at some velocity, causing them both to stick together and the bar-ball pair to rotate about the new center of mass. About ...
2
votes
1answer
150 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 ...
0
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1answer
46 views

Rotational dynamics about a point or an axis?

In several books and sites, its written that torque is calculated about an axis and angular momentum is calculated about a point. In MIT's Angular momentum lecture pdf, Angular momentum has been ...
2
votes
1answer
119 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 ...
0
votes
1answer
154 views

What forces cause the centripetal acceleration in circular motion on a merry-go-round?

Suppose you stand on a merry-go-round spinning at $f$ revolutions per second and you are $R$ meters from the center. What forces act on you? If you were tied to a rope like in Fig 2 you would follow ...
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1answer
74 views

Can moment of inertia be defined as function of mass?

For continuous bodies, moment of inertia is found as $$ \int dI = \int_{m_i}^{m_f} r^2(m) .dm$$ . Now, $$\int dx = \int_{u_i}^{u_f} f(u).du \implies X_f(u) = \int_{u_i} ^{u_f} f(u) .du + X_i(u)$$ , ...
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votes
2answers
59 views

Computing lengths for a rotating rod

I know how to assign dimensions to a profile that is under static loading - that is under Mechanics of Materials, I would agree on a beam section, calculate the maximum moment and use the elasticity ...
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0answers
15 views

Spinning top don't fall and stationary one can't stay upright [duplicate]

Why a spinning top do not fall but a stationary one falls. What kind of law is governing it.
2
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2answers
303 views

Why does an unhinged body rotate about its centre of mass?

If a force is applied to a body which does not act through its centre of mass, it rotates about its centre of mass and not any other point. Why?
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3answers
423 views

Minimum angular velocity for circular motion (pendulum)

How can I show that there is a minimum angular velocity $\omega_{min}$, different from zero, such that if we chose an $\omega$ smaller than $\omega_{min}$, then it is not possible to have a circular ...
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2answers
102 views

Flipping a bottle

I tried to do this experiment recently at school and my house. I started the experiment by having three same type of bottles with the labels A,B and C. Bottle A has been fully filled with water, ...
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0answers
24 views

How to prove the relation between the rate of change of a vector in space coordinate and in body coordinate?

I'm learning Goldstein's classical mechanics, and in chapter 4.9 he prove such an operator equation $(\frac{d}{dt})_s=(\frac{d}{dt})_r+\omega \times$ In the proof, he takes the space and body axes as ...
0
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1answer
35 views

How to approximate lag of roll of a bird (or RC airplane)?

When an airplane rolls using ailerons, the ailerons itself are changing their state quite instantly. However, in order for the airplane to actually start to roll, it should take a considerable amount ...
0
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2answers
52 views

Rigid bar on the floor of a rotating space station

I read this in a comment to an answer in physics.stackexchange.com. The comment was An easier method might be to just place a straight, rigid beam on the floor. If you find the floor is concave, ...
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0answers
29 views

Most general gyroscope motion [duplicate]

In Kleppner & Kolenkow's Introduction to Mechanics (Amazon link), the general gyroscope motion including nutation was derived using the approximation condition $\Omega T \ll 1$ where $\Omega$ is ...
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4answers
329 views

Why is moment of inertia dependent on $r^2$ and not on $r$ ? (physical reason)

Moment of inertia is the mass equivalent in rotational dynamics. I know , by mathematical arguments, moment of inertia of a particle is $$ I = \text{mass} \cdot r^2$$ . But what is the physical ...
3
votes
1answer
817 views

Ball Rolling Down An Inclined Plane - Where does the torque come from?

There is a ball rolling down an incline, with no slipping. If we consider the point of contact between the ball and the inclined plane to be the pivot point (for our torque calculations), then I have ...
1
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1answer
92 views

Disk and Ball on a smooth surface [closed]

A uniform disk of mass $\text{2m}$ and radius $\text{R}$ is placed freely on a smooth surface as shown in the figure. A particle of mass $\text{m}$ is connected to the circumference of the disc with a ...
3
votes
2answers
595 views

Can moment of inertia be negative? [closed]

Q: Find out the moment of inertia of a uniform circular disc of radius $r$ & mass $M$ & the axis passes through a point on the circumference. My attempt: Let the axis passes through $O$ on ...
1
vote
4answers
203 views

Rotation systems. Problem interpreting an equation

In this equation: $$ \mathbf a_i\overset{\rm def}{=}\left(\frac{d^2\mathbf r}{dt^2}\right)_i=\left(\frac{d\mathbf ...
21
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6answers
9k views

Can a car steer on a frictionless surface?

Do the front tires of a car act like gyroscopes, such that a car could steer on a frictionless surface?
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3answers
169 views

Forces and acceleration on rotating objects?

Suppose you have an object undergoing uniform circular motion, with force vector pointing towards the center and another force vector tangential. Can it be said that the net force pointing in the ...
4
votes
3answers
484 views

Has a body angular momentum and torque only in a circular path?

In different contexts, my book(Principles of Physics by Resnick, Halliday ,Walker) , they wrote For torque, the path need no longer be a circle and we must write the torque as a vector ...
1
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1answer
182 views

If direction of torque is upwards(or downwards), why does the body rotate perpendicular to the direction?

We know torque is given by $$\vec{\tau} = \vec{r} \times \vec{F}$$ . Its direction is given by right-hand rule which says that torque acts perpendicular to the plane where force applied and position ...
1
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3answers
76 views

Problem in understanding the process of calculating the rotational inertia

As we know, rotational inertia is the mass-equivalent in rotation. For a discrete body, it is measured as $$I = \sum m_i{r_i}^2 $$ . But when a continuous body comes, $$I = \int r^2 .dm$$ which ...
1
vote
1answer
56 views

Why does a rolling disc topple less easily than a standing one?

If a force is applied perpendicular to the surface of a disc it topples sideways. Also, a stationary disc topples more easily than a rolling one. The explanations I've seen for this state that since ...
0
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0answers
29 views

Force and Torque being applied off-center due to magnetic forces [duplicate]

Say that I have two magnetic dipoles, one of which is rigidly attached to a freely movable inflexible body at some point that is not at the body's center of mass, while the other is fixed in space. ...
1
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3answers
773 views

Will an object rotate when we apply a force to it?

What would happen if the axis of rotation passes through the centre of mass of an object? Will the object rotate when we will apply a force to the object? Edit: The object is free, is not fixed to an ...