# Questions tagged [rigid-body-dynamics]

The study of the movements of a collection of connected bodies subject to external forces in the absence of deformation. This tag should be used for questions on the analysis of 2D/3D dynamics of rigid bodies, do NOT use this tag because your question contains a rigid structure.

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1 vote
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### Moment of inertia of irregular object

How could you use a torsional pendulum to determine the rotational inertia of any object that could be mounted on the Rotary Motion Sensor?` Note: The Vernier Rotary Motion Sensor is a bidirectional ...
1 vote
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### Experimentally determine the Moment of Inertia of a complex (mathematically indescribable) object

I'm a high schooler that's trying to design a robot for a physics project. The robot is a catapult; it will calculate a trajectory and shoot at a certain speed and angle using a large motor. I'm using ...
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### Reference request - book on Euclidean space and rigid body kinematics

Ideally, I'd like a comprehensive book that encompasses both subjects: it builds the notion of "space" as related to our physical world (no relativity, though) from the ground up, giving it ...
1 vote
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### Work done by an eccentric force on a rigid body

I am hoping someone can explain in simple terms where I might be going wrong in my logic below. We have a thin rigid rod (see diagram A) where a couple is acting and rotates the rod about its COM by ...
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### Why static friction is necessary for pure rolling instead of kinetic friction?

Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity $v$ and zero angular velocity. the kinetic friction would be applied between the ...
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### Role of static friction in rolling

I am confused as to how does static friction (analytically) causes rolling motion. As far as i understand For causing a rigid body to rotate about its centre of mass a torque must displace angularly, ...
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### What are the steps to the approximation for this falling pendulum problem?

I am trying to understand the math here. How long would it take for an upright rigid body to fall to the ground? But I am lacking in some basic mathematical concept/techniques. In several answers, an ...
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### Pure rolling with two contact points [closed]

When a sphere is rolling on a sufficiently rough surface we use conditions such as V= rω But what conditions can we apply for a system where sphere is in contact with two points on the stationary ...
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### 6 DoF rigid body equations and tensor of inertia

I am writing here as I have a doubt on the tensor of inertia found in the Euler's equations. As far as I have understood, people usually solve the Euler's equations in "body coordinates" as: ...
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### Quasi-rigid bodies in relativity and decomposition of energy

In relativity there can be no perfect rigid solids, the Born rigidity is as close as you can get and yet it is severely constrained (Herglotz-Noether theorem). For that reason, rigid solid mechanics ...
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### Magnitude of the time derivative of angular momentum

This is a problem involving a stick of mass m and length l which spins with frequency ω around an axis, as shown in the figure below. The stick makes an angle θ with the axis The goal was to find the ...
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### Moment of Inertia of Higher Dimensional Objects

I would like to take on the mathematical exercise of deriving expressions for the moment of inertia of higher dimensional solids. But could there be any real world utility to it? If yes, which fields ...
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### How can precession produce a torque in the direction of precession when it has no angular momentum?

I this video, an 8 lb gyro on a rod supported at one end is spun up to several thousand rpm, and an assist is use to get the axis nearly horizontal. A small stick is used to nearly instantly stop the ...
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### Quantum Mechanics of a rigid body that has only finitely many possible axes of rotation

I consider the quantum version of dynamics of rigid body motion with intrinsic angular momentum, having moment of inertia $I$. Given a classical free system of one free rotating spherical rigid body (...
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### Two questions regarding Spivak's Configuration Space

The following is from the fifth Chapter Rigid Bodies of Spivak's Physics for Mathematicians. The post consists of a statement Spivak makes -with no proof- that I do not understand. For clarity, I've ...
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### Moment of Inertia Tensor and Center of Mass

Can the Moment of Inertia Tensor be diagonal in a reference frame where the Center of Mass of the system is not on some of the axes?
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### Does the intermediate axis theorem violate angular momentum conservation?

According to the intermediate axis theorem, an object rotating about its intermediate axis with a very slight perturbation will undergo periodic flips in its orientation in the absence of external ...
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### What is wrong in this derivation of centre of mass of hollow hemisphere [closed]

I am trying another method to find centre of mass for hollow hemisphere.the treatment is as for solid hemisphere but in this case the answer goes wrong i can not found out what is the problem. Please ...
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### Direction of angular velocity vector VS angular momentum vector

I understand that angular velocity and angular momentum velocities don’t need to be parallel to each other. However, I’m confused what these vectors even represent. So I have 3 questions about this: ...
1 vote
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### How to calculate degrees of freedom?

Background I am trying to run optimizations on a multilink (car-) suspension. That is each link is defined by two points, one on the vehicles body, one on the wheel mount. There are 5 links in total, ...
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1 vote
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### Confusion about the Spinning Top

Consider the following symmetric spinning top with a fixed point on the horizontal surface. I have two questions concerning its motion: let $\underline{\Omega}$ denote the precession angular ...
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### Why don’t we treat rigid bodies as particles only [closed]

We know the law $F_{net}=ma$ is for a particle. But for rigid bodies we have another law that includes COM ie $F_{ext}=Ma_{com}$. It’s done because there is rotational motion with translational which ...
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### Why do internal forces in a rigid body do no work? [duplicate]

Why is the work done by the internal forces in a rigid body zero? Most proof's for that sort of thing seem to assume that the internal forces in the rigid body are in the line attaching the points in ...
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### When to apply $I_c \underline{\omega} = \underline{M_c}$?

I was solving an exercise the other day, about a rolling cylinder on an inclined plane. Initially the cylinder slides, but then it begins to roll and the problem wanted to know the velocity of the ...
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### Why do we talk about inertia tensor?

When we talk about the inertia of a rigid body, in calculating the angular momentum as a function of the moment of inertia and angular velocity, the inertia tensor is introduced. But why is it a ...
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### Why do these two methods give different answers? MOMENT OF INERTIA [closed]

A question and a figure are shown in the image below. MOI—MOMENT OF INERTIA COM—CENTER OF MASS In my attempts to answer this question, I discovered two approaches: The first method entails the ...
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### When we say a rigid body is a system of particles, what exactly are 'particles' here?

In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
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### Angular Momentum of asymmetric physical pendulum (Rigid Body)

The angular momentum of a rigid body respect to a pole $O$ located on its axis of rotation $z$ is uniquely determined if we know its angular velocity: \$\vec{L}_O = I_z\vec{\omega} - \omega\iiint_V ...
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### How would a rigid disk rotating near speed of light behave? [duplicate]

Say you had a perfectly rigid disk so that you can't morph it or bend it. If you were to spin near the center of the disk at near speed of light, the edge of disk would have to be faster but of course ...
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1 vote
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### Will the puck rotate without slipping in this situation?

We have two pucks moving on a plane without friction. On one of them a force is applied on it's center of mass. On the second a force of equal magnitude is acting tangential to the puck and at a ...
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### Angular velocity of point on rigid body [duplicate]

a while back I asked this question and I still did not fully understand. Suppose we have a rigid object rotating about some central point with a given linear and angular velocity, how do we then ...
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### Number of Degrees of Freedom of a Rigid Body System - Proof

Let us define the number of degrees of freedom of a material system as the number of scalar parameters needed to know the position of each particle of the system with respect to any inertial frame of ...
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### Doubt in Equations of motion of rigid body, can anyone tell me how the second step occurred from first one [closed]

Doubt in Equations of motion of rigid body, can anyone tell me how the second step occurred from first one.
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### Conservation of energy in a rigid body

"One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance. The other end of the rod is held still so that it touches the ...
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### Is work done by torque due to friction in pure rolling?

This question has been asked and answered numerous times. I went through almost all of them and found no consensus. I found that all of the answers can be divided into two categories: Friction does ...
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1 vote
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### Euler's Angles and Uniquely Defining the Orientation of a Rigid Body

When speaking about the orientation of a rigid body, Symon (Mechanics, 3rd ed.) writes: It turns out that no simple symmetric set of coordinates can be found to describe the orientation of a body, ...
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### How do the inertia tensor varies when a rigid body rotates in space?

The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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### When two systems of forces acting on a rigid body are equivalent?

My book says that "it is clear that if you replace the system of forces with a second system having the same resulting force and the same resulting moment, with the same initial conditions the ...
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