A tag for questions about rotational motion, including angular velocity and angular acceleration.

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1answer
341 views

Calculating Angular Acceleration of a Rolling Object

A bowling ball of mass M = 6.50 kg, radius R = 10.0 cm, and moment of inertia I = $(2/5)MR^2$ is given an initial center of mass velocity $v_0 = 3.00 m/s$ that is parallel to a horizontal surface. ...
3
votes
1answer
180 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
2
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3answers
2k views
2
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2answers
120 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
2
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3answers
4k views

A simple derivation of the Centripetal Acceleration Formula?

Could someone show me a simple and intuitive derivation of the Centripetal Acceleration Formula $a=v^2/r$, preferably one that does not involve calculus or advanced trigonometry?
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3answers
23k views

What is the difference between angular speed and tangential speed in a circular motion?

I was looking a long time for the way the equations of this two speeds are obtained, and i found pretty much nothing important, so can someone explain how are those obtained, and which is the ...
2
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3answers
2k views

If angular velocity & angular acceleration are vectors, why not angular displacement?

Are angular quantities vector? ... It is not easy to get used to representing angular quantities as vectors. We instinctively expect that something should be moving along the direction of a ...
2
votes
1answer
161 views

Why is the inertia ellipsoid of a higher symmetry than the rigid body?

I was always puzzled by this fact. A uniform cube has a sphere-shaped inertia ellipsoid. The sphere has a higher symmetry then the cube. Is there any deep reason or implication behind it?
2
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3answers
316 views

How do I know what variable to use for the chain rule?

In my textbook the tangential acceleration is given like this: $$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$ $$a_t=rα$$ I understand that the chain rule is applied here like this: ...
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2answers
1k views

Piston movements in four stroke cycle?

I was reading about a four stroke cycle. Here's what I understood: In the first stroke, the piston starts at the top and moves down. In the second stroke, the piston moves upwards. In the third ...
2
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1answer
125 views

Why does this model fall apart when angular velocity is small?

I'm doing a physics problem in which a marble spins around a spinning bowl and both have angular velocity $\omega$. It rotates with radius $r$ around the central axis and the hemispherical bowl has ...
2
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3answers
2k views

Angular momentum equations

I do not understand this because angular momentum is $L=I\omega$ ($I$ is moment of inertia;$\omega$ is angular velocity) but it I have also seen equations where $L= rmv\sin(x)$. I do not understand ...
2
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1answer
4k views

Merry go round physics problem?

So I have the following statement. "A merry-go-round is spinning with a fixed angular speed. As a person is walking towards the edge, the force of static friction must increase in order for the ...
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4answers
455 views

Rotation axis of a rigid body

I am confused about a trivial concept. Let the rotation of a rigid body, say with one point fixed, be described by the equation $\vec{x}(t)=R(t)\vec{x}(0)$, with $R(0)=I$. Then, at each instant ...
2
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1answer
947 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?
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5answers
55 views

Two identical disks pulled differently question (Kinetic Energy)

I am currently taking a basic physics course in college and I am having a bit of trouble on this problem that deals with rotational and translational kinetic energy. Let's begin: The question: The ...
2
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2answers
81 views

Calculating moment of inertia for a cylinder?

I'm trying to calculate the moment of inertia for a cylinder about a longitudinal axis, but I don't know where I went wrong with my approach. $$I=\int r^2 dm$$ Assuming constant density: ...
2
votes
1answer
105 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
2
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3answers
302 views

Sign of torque when rolling an object down an incline

Suppose you have an object rolling down the incline at 30 degrees. Given the point of contact is instantaneously at rest, I decided to analyse torques at that point. Therefore, the only force ...
2
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1answer
142 views

Why is the Earth self-rotating? [duplicate]

What drives this happen? Would it be the internal energy or by an external force? I did try to Google the answer, but could not find a good one.
2
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2answers
289 views

What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?

Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
2
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2answers
250 views

Non-constant angular velocity

In this paper about Backstepping controll of a quadrotor helicopter an algorithm for control is described, but I have hit a dead end. In equation 15 it is described the part of state space for the ...
2
votes
1answer
212 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
2
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2answers
430 views

Angular Momentum of a rigid, extended object

Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum. It is often said that an object that has been thrown up in the air ...
2
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1answer
175 views

Kinematics of Euler angles relative to a rotating frame

I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and ...
2
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2answers
721 views

Rolling of a disk and sphere

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has ...
2
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3answers
2k views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
2
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1answer
37 views

Asking about centrepetal acceleration

please look at the fig first 1) How can you claim that the triangle ABC is same as the triangle PQR? 2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB? ...
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1answer
1k views

How does weight/mass affect angular momentum?

How does weight/mass affect angular momentum? For my 8th gr science fair project I have to do an experiment on angular momentum. My problem is that we have not been taught any of that in physics yet, ...
2
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1answer
577 views

Relating angular and linear kinematics

In my physics book "University Physics", there is a chapter on relating linear and angular kinematics. I understand the parts where it shows $v = r\omega$ and $a_{\text{tan}} = r\alpha$. However in ...
2
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1answer
5k views

What's the right way to calculate the principal moment of inertia?

I am writing a program that incorporates calculating the principal moment of inertia for a protein residue based on its component atom XYZ coordinates. I am exceedingly confused about which formulas ...
2
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5answers
1k views

motion in the body-fixed frame?

This is really basic, I'm sure: For rigid body motion, Euler's equations refer to $L_i$ and $\omega_i$ as measured in the fixed-body frame. But that frame is just that: fixed in the body. So how ...
2
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1answer
190 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and ...
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0answers
46 views

Unruh radiation in a rotating frame

Unruh radiation normally applies to linearly accelerated frames Is there an equivalent of the Unruh thermal radiation in a frame that is spinning? I am not aware of any horizon being created from a ...
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2answers
95 views

A Confusion in Rotational Dynamics

I am trying to analyse the following situation using classical mechanical concepts. Consider a a straight rod $AB$ of mass $M$ and length $L$ placed on a frictionless horizontal surface. A force $F$ ...
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0answers
92 views

Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”?

I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other ...
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0answers
45 views

Would a large, small mass object in orbit experience induced rotation

Imagine a large (multiple earth radii), very small-mass ring orbiting The Sun. Half of the ring would be closer to The Sun than the outer half. Since orbital velocity decreases with distance, two free ...
2
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1answer
653 views

Integration on a general equation for instantaneous angular acceleration

An equation for instantaneous angular acceleration is given as: $$ \alpha \equiv \lim_{\Delta t\to0}\frac{\Delta \omega}{\Delta t} = \frac{d\omega}{dt} $$ The text I am reading says writing this ...
2
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1answer
546 views

Equations of motion in 2D [closed]

I'm struggling with a seemingly simple problem in 2D motion. Basically, the question is, given accelerations in $x$ and $y$ ($a_x$ and $a_y$) as well as the angular velocity ($\omega$), how can we ...
2
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1answer
371 views

Paradox of the Relativistic Record Player [duplicate]

Possible Duplicate: Invariant spacetime - distance - Circular Motion This is a question that I thought up a few years ago when I was taking mechanics. I asked the professor but didn't ...
2
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1answer
154 views

Why do some objects tend to change their axis of rotation while rotating?

This question struck me a few minutes back, I was at a table with a pear. It was more narrow than round.I proceeded to rotate this pear in one swift movement. It rotated for a few seconds, and ...
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2answers
2k views

force applied not on the center of mass

When applying a force outside of the center of mass of the body, the body will get both linear and angular momentum. Right? Does the linear velocity from this force equal to the linear velocity from ...
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5answers
2k views

Why can mass not be considered concentrated at CM (center of mass) for rotational motion?

Could anyone explain the following expression: Why can mass not be considered concentrated at CM (center of mass) for rotational motion?
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3answers
255 views

Does circular motion cause centripetal force OR does centripetal force cause circular motion?

Does circular motion cause centripetal force, or does centripetal force cause circular motion, or are they both occurring hand in hand together instantaneously? One more question: If I project a body ...
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3answers
42 views

Why the similarity in the Equations of Motion for Rotational and Rectilinear Motion?

These are the equations of motion given constant acceleration, for first rectilinear and then rotational motion. Rectilinear Motion: Rotational Motion: While the variables have changed, and the ...
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2answers
278 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
1
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1answer
307 views

What kind of physical quantity is angular displacement?

Angular Displacement is neither a vector nor a scalar. What type of physical quantity it is? Are there any other examples of that physical quantity?
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1answer
910 views

If I jump will I land in the same spot? [duplicate]

If I were to jump one meter in the air and hang for one second, would I fall back down in the same spot or would the earth rotate ever so slightly under me, causing me to land a short distance away ...
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2answers
3k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
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2answers
49 views

What is the purpose of the directions for vector quantities such as angular velocity and torque?

Looking at just both angular velocity and torque, many other exhibit this same property. What is the purpose of and usefulness of having a direction that is in the Z-direction? (assuming that, in the ...