1
vote
0answers
46 views

point-particle vs rigid-body [closed]

As pointed out here point-particle-based modeling can lead to very inaccurate predictions. Could you give an example where point-particle-based model describes reality accurately enough and one where ...
4
votes
1answer
75 views

How to simulate rotational instability?

I'm trying to simulate (for an educational game) the well-known effect that rotating objects with three nonequal moments of inertia are unstable when rotated around the middle axis. Some explanations ...
2
votes
1answer
55 views

Converting Point Gradients to Rotational Representation

I'm a PhD student in an unrelated field. It's been a very long time since I've done physics, and I've run into a problem in my research which I think is actually a physics problem. Basically, I have ...
0
votes
1answer
52 views

Finding the minimum radius of the pivoted disc

Here is a question based on Simple Harmonic Motion that I tackled just now. However I think I am having an approach to tackle this but I am not sure about it. Ouestion: A uniform disc of radius ...
0
votes
0answers
26 views

How do two rigid bodies with different 3rd moment of inertia rotate differently?

If rigid bodies $R_1$ and $R_2$ has exactly same total mass $M$, central of mass, and rotational inertia $I$, but different third moment of inertia $M_3$, how would they move/rotate differently? ...
8
votes
1answer
504 views

Defy gravity torques with gyroscopes?

Context On the following drawing, a platform is hung from the ceiling not exactly from its centre of gravity. Because of this it can't sustain an arbitrary orientation for long; I want to increase ...
3
votes
4answers
195 views

Solving for motion of rotating rod using only Newton's laws?

I have a question that's been bothering me for years. Given a rod of uniform mass distribution with total mass $M$ and length $L$ that lies on a horizontal table (with one end fixed to the table ...
0
votes
1answer
61 views

Question about the parallel axis theorem

I've a question about the parallel axis theorem. So I'm perfectly OK with the derivation of the proof in 2D. However in the typical derivation they just say this in my textbook "Because the Zi ...
1
vote
0answers
49 views

A rigid rotating rod that breaks in two pieces

Suppose we have a rigid rod of lenght $L$ and homegenous mass density. One of its extreme points, say $P$, is fixed so that the rod can rotate around the axis passing in it. Initially the rod is held ...
0
votes
1answer
59 views

Balancing stick on hand - inverted pendulum motion

How do I calculate the velocity and acceleration of a stick that is vertically on my hand? How fast and far do I need to move my hand from side to side to keep balancing the stick? Assuming that we ...
3
votes
2answers
117 views

Consider a horizontal surface with or without friction. Ideally, will a wheel rolling without slipping roll forever in both cases?

Suppose a wheel is rolling smoothly on a horizontal plane i.e., it is rolling without slipping. Now let's take the two cases of the horizontal plane: It has friction It is frictionless In the ...
1
vote
1answer
41 views

Is there no problem in thinking of any motion of a rigid body as a composition of translational motion and rotation w.r.t center of mass?

Sometimes when I work on mechanics problems, I wonder if this analysis is always valid. Couldn't there be some motion of a rigid body that cannot be expressed as a composition of translational ...
0
votes
0answers
156 views

Calculating Inertia Tensor with Parallel Axis Theorem

Say you have a solid you are approximating as n point masses at different points in a 3D space. Each point mass has a mass of 1. The origin is not the center of mass. All the points have location ...
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. ...
0
votes
2answers
280 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'}, ...
0
votes
1answer
48 views

Force on a line

Say you have a rigid line of mass $m$ and length $\ell$ along the $x$ axis and you apply a constant force $f$ at one end in a direction that is always perpendicular to the line, starting in the $y$ ...
0
votes
2answers
71 views

Rigid body rolling quesion

Hey, im having a bit of trouble with the problem in the added photo. So, there is the cylinder which is attached by a massless rope to a massless pulley, to a box (assume it is a pointed object). ...
3
votes
1answer
131 views

Understanding gyroscopes

Considering the typical situation of a rotating bicycle wheel held by one end of its axle by a rope tied to the ceiling: gravity torque is the time derivative of the angular momentum, and in this case ...
2
votes
2answers
221 views

Rod Falling on Frictionless Surface

A rigid rod with mass m is initially held at an angle with respect to a frictionless plane by a string. Then the string is cut. What happens to the rod? My intuition suggests that the rod should slide ...
1
vote
4answers
138 views

Centre of instantaneous rotation problem

Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
1
vote
2answers
125 views

Rigid bodies - the wheel

As I've been taught lately in my mechanics course: the wheel has a unique property: at every moment of motion, the touching point between the wheel and the ground is not in movement and ...
0
votes
1answer
56 views

How does this formula for calculating the “mass sum” in a collision translate to 3D?

According this tutorial, formula number 5: $$j = \frac{-(1 + e)((V^{A} - V^{B}) * t)}{\frac{1}{mass^{A}} + \frac{1}{mass^{B}}}$$ translates into formula number 6: $$j = \frac{-(1 + e)((V^{A} - ...
1
vote
1answer
197 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 ...
2
votes
3answers
265 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 $v_0$ ...
10
votes
3answers
469 views

What is the physics of a spinning coin?

When we spin a coin on a table, we observe 2 things: It slows down and stops after sometime. It does not stay at just one point on the table but its point of contact with table changes with time. ...
0
votes
1answer
130 views

2D. Force applied at angle to body, where translational vector will be directed?

I'm not a physicist and just making some research by the way of creating simple physics simulator, because of that, sorry if this is very dumb question, but I really need help with it. Let's assume ...
0
votes
0answers
83 views

How can I simulate a rigid bounced from a wall?

How can I simulate a rigid sword bounced from a wall and hit the ground(like in physical world)? I want to simulate a simple animation. The sword is controlled by a center/mass point.(Actually ...
2
votes
1answer
573 views

How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?

For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?
-1
votes
1answer
275 views

A Rolling Quarter [closed]

A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $R=4 \text{cm}$. The plane of the coin is tilted at an angle of $\theta=45^{∘}$ with ...
16
votes
3answers
2k views

Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions ...
3
votes
2answers
211 views

Extension to continuous in proofs of rigid body mechanics

I'm studying rigid body mechanics and I've seen several proofs of properties related to total angular momentum, kinetic energy, etc. that all regard discrete set of points. For example, to show that ...
7
votes
6answers
9k views

What do people actually mean by “rolling without slipping”?

I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain. I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational ...
3
votes
1answer
1k views

Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating ...
5
votes
7answers
1k views

What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?

Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating ...
1
vote
2answers
535 views

Kinetic energy of a cylinder

It is a long cylinder (you can approx $R=0$), and it has a fixed point in one os its ending points, it's rotating on a plane and I have to calculate the kinetic energy from reference systems situated ...
1
vote
2answers
174 views

Unexpected potential energy increase during Tic-Tac drop

I dropped a Tic-Tac: (no worries, it happened before), and I noticed as it bounced on the floor that it would first jump 20 cm high, and at the next bounce for instance 50 cm high. Shouldn't it ...
1
vote
2answers
579 views

How are Euler's laws of motion applied to gyroscopes?

Euler's laws of motion for a distributed mass are: $$F = \frac{d}{dt} MV_{cm},\ N = \frac{d}{dt} L$$ $F$ are the sum of the external forces, $M$ the total mass, $V_{cm}$ the velocity of the centre ...