The time derivative of angular position used when studying rotating objects or systems.

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How do I find the linear components of acceleration in a pendulum?

I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
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1answer
61 views

Why is angular acceleration of a pendulum always negative?

I was trying to derive using the Lagrangian the equations of motion of a simple pendulum under the influence of gravity. Eventually, I was brought to this conclusion: $$\alpha = -(g\sinθ)/l$$ where ...
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1answer
30 views

Why do we represent the axis of rotation using vectorial notation [closed]

When a body (in pure rotation) rotates along an axis passing through it, why do we represent the axis of rotation in vectorial notation? Wouldn't it be sensible enough to represent the angular ...
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1answer
31 views

Rotation and Momentum

I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector. However, is it correct ...
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2answers
57 views

What is the dimensional formula of angular velocity?

I have problem to determine the dimensional formula of angular velocity. My friend said that the dimensional formula of angular velocity is $T^{-1}$. It's come from rad/s, rad is dimensionless, the ...
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1answer
45 views

Lagrangian in polar coordinates [closed]

$$L=\frac{1}{2}mv^2=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)$$ $$L=\frac{1}{2}mv^2=\frac{1}{2}m(\dot{r}^2+r^2\dot{φ}^2)$$ I dont get this part. ...
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2answers
32 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
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1answer
68 views

What is $\omega \times v$?

I found that equation in my textbook. It says that $\omega \times v$ ($v$ is velocity) is centripetal acceleration. But how is the equation derived?
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2answers
85 views

Centripetal force: if radius decreases, does ANGULAR or TANGENTIAL velocity change?

Having conceptual trouble with this aspect of centripetal force. Say we have a puck on a frictionless table attached to a string that I am holding through a small hole, so that the puck moves in a ...
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2answers
74 views

Angular momentum of rolling sphere [closed]

A sphere of uniform density $\rho$ and radius $r$ is rolling without slipping on a perfectly flat surface. It is moving in a perfectly straight line and its axis of rotation is parallel to the plane ...
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2answers
36 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...
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3answers
59 views

Rotation of rigid body with two different angular velocities

Consider a cylinder that rotates about a vertical fixed axis with angular velocity $\vec{\Omega}$ while rotating about a vertical axis passing through its center of mass with angular velocity ...
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1answer
109 views

What happens to a ball spinning with peripheral speed near to the speed of light?

I can't imagine such phenomenon. Would it becomes an ellipsoid, or maybe a straight line?
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1answer
19 views

Angular velocity and velocity of CM indipendence in rigid body motion

In the most general case, in rigid body motion the linear velocity of the center of mass $v_{cm}$ and the angular velocity of the rigid body $\Omega$ are not related with each other. Which condition ...
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2answers
37 views

Proof derivative of a vector following precession motion

I do not get some points of this proof about the time derivative of a unit vector $\hat{u}$ (costant magnitude) which is following a precession motion. The picture is the following. I want to ...
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2answers
28 views

Velocity of the points of a rigid body

The most general motion of a rigid body is a roto-traslation. Firstly is it correct that any point (let's call it $O$) of the rigid body can be seen as the point through which passes a istantaneous ...
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1answer
33 views

Component of angular momentum perpendicular to the rotation axis in rigid body rotation

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation ...
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1answer
32 views

Proof of constant angular velocity in rigid body motion

I'm studying rigid body motion on Landau but I'm having troubles to understand this proof of the fact that the angular velocity $\vec{\Omega}$ is constant for a rigid body. My doubt is about the ...
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0answers
40 views

Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity ...
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1answer
42 views

Why will kinetic energy decrease?

Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ...
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2answers
58 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
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0answers
43 views

Converting torque to angular velocity

Given the torque of a system, is it possible to convert this torque to the angular velocity of the object? I calculated the torque exerted by wind on a blade, however, now I need the RPM. To get the ...
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1answer
43 views

How does angular velocity transform on the surface of a sphere?

If we consider the earth as a sphere than it will have an angular velocity of $\boldsymbol{\omega}=\omega\mathbf{e}_z=\frac{2\pi}{T}\mathbf{e}_z$ where $T\approx24h$. Now we have given a location in ...
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24 views

Angular velocity in body frame to displacement in lab frame?

For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis: $$ \omega_1 = w_1 \cos (w_3 t) $$ $$ ...
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1answer
24 views

Solid Body Rotation: ω in radians/second or rotations/second?

I am just wondering if I use the solid body rotation equation rotational energy = 1/2mr^2ω^2 and I solve for ω, and then plug in numbers, does the ω come out in radians/second, in rotations/second, ...
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1answer
44 views

Angular acceleration from torque and radius

The story is about wheel. I have a wheel and I need to know it's actual angular velocity(which doesn't mach Vcar_longitudal / r). What I have access to is torque ...
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1answer
49 views

Why doesn't this differential derivation of the centripetal acceleration formula work?

I wanted to derive centripetal acceleration from scratch and tried using differential equations. But no matter what I did I hit a snag as follows: $\alpha=$ centripetal acceleration $\omega=$ ...
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1answer
57 views

Calculating Rolling friction of a car's wheels (NOT ON AN INCLINE)

I'm dealing with a small toy car consisting of a bottle that has a small hole in the back, covered by a thumb tack. The bottle is filled with pressurized air then the thumb tack is released, releasing ...
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2answers
114 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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1answer
49 views

Angular velocity when a rod inclined to a wall slips and its subsequent motion observed from the axis of rotation

When a rod inclined to a wall slips, rate of change of which angle does the angular velocity represent? Is it the rate of change of angle with which the rod is inclined to the horizontal ? I'm not ...
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1answer
88 views

Conservation of angular momentum of system of two objects

This may be a silly question, but I just want to clarify something. Say we have two spinning spheres, each spinning about an axis going through their own center of mass: All of the conservation of ...
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4answers
138 views

Spinning disk touches stationary disk [closed]

Suppose we have a solid disk of mass $M$ and radius $R$ that is spinning at an angular velocity of $\omega_0$ about an axis going out its cm. It is brought to touch a stationary disk of mass $m$ and ...
2
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2answers
28 views

What is the relation between centripetal acceleration and radius in uniform circular motion?

In uniform circular motion we know that $a_c=\frac {v^2}r=\omega^2r$.So,is $a_c$ directly or inversely proportional with $r$ and why not the other is true? Thanks for any help.
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1answer
58 views

How can a particle in circular motion be in translational motion?

I came across this: If a particle is moving in a circle it is in pure rotational motion about the centre of the circle, while for a moment it may be in pure translational motion about some other ...
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1answer
44 views

Angular Velocity of Semicircle [closed]

In a 2-Dimensional world, a semicircle with center O, mass M and radius r is placed on the ground, with C as the point of contact. A small beetle of mass $m$ is placed at C which starts walking ...
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2answers
92 views

fortune wheel - angular acceleration, given initial velocity, radius, angle

I have another physics problem and I'm trying to solve this using formulas I found on the web. I'm an online student and there is no textbook given for our course nor is the topic explained in the ...
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0answers
51 views

Correct formulas for two wheeled robot motion

I'm trying to write a simulation of a two wheeled robot, which can be controlled by varying the speeds of his wheels, independently. However, the physics engine that I'm using can only rotate a body ...
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1answer
161 views

Change in acceleration due to gravity because of rotation of earth [duplicate]

The formula above is the equation for acceleration due to gravity when earth rotates. G is the original acceleration. Can someone explain how this formula came?
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3answers
288 views

Is angular velocity parallel to axis of rotation?

I'm reading the Wikipedia page on angular velocity. It says here of the angular velocity vector in three dimensions that “[t]he magnitude is the angular speed, and the direction describes the axis of ...
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0answers
24 views

How can I calculate the torque of draw force which affect on spinning ball flying in the air?

I am studying the Magnus effect on a flying ball i have calculate the magnus force but i trying calculate the angular acceleration, because the angular velocity of the ball is not constant. I have ...
2
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1answer
139 views

Calculating acceleration offset by C.G [duplicate]

I'm trying to calculate the acceleration an accelerometer would read NOT placed in the Center of Gravity of the object. Let's look at the figure below (or in link provided). The accelerometer was ...
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1answer
58 views

Time dilation at the Innermost Stable Circular Orbit

According to general relativity the time dilation is given by following formular: $d \tau = \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}$ If I'm interestet in the time dilation at the ISCO I set ...
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1answer
29 views

Why does a ball rotate sometimes when you throw it?

My guess is that when you throw a ball, which is held by your hand, using you arm, the radius of the circular path being constant, the outermost part of the ball has a bigger radius than the innermost ...
0
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2answers
110 views

angular velocity of rigid body

I am doing some physics for a game. I have a rigid body defined as multiple balls of the same mass distributed to make some object. Let's say I put to each ball a different velocity but because it is ...
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0answers
29 views

Total angular velocity (Kerr metric)

I have a problem with the kerr metric and the "rotating spacetime" in the ergosphere. How can i calculate the angular velocity $\omega$ of an object in the ergosphere (which flys from infinity into ...
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3answers
72 views

Angular velocity from orientational displacement

A 3-dimensional object is rotating around an unknown 3-dimensional axis through the object's center of mass. Its orientation is described by two unit vectors. I know an initial orientation and a final ...
0
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1answer
16 views

Which part of an angular velocity vector is its direction?

I am assuming that an angular velocity vector only has two direction: positive for counterclockwise and negative for clockwise. Just to make sure that I have the right interpretation. Newton's 1st ...
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1answer
40 views

Direction of angular velocity

please help me here! Im confused, is direction of angular velocity perpendicular to the plane of motion, or along the plane of motion?? From hyperphysics - ...
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1answer
184 views

How do you calculate theoretical ratios of angular velocity final and angular velocity initial? [closed]

I'm asked to calculate the "Theoretical Ratio". ($\omega_f/\omega_i$) I have Inertia of the Disk = $I_{DISK} = .0094115713$, I have Hoop Inner Radius = $I_R = 55.725$ So I am supposed to use the ...
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0answers
32 views

How rotational force calculation depends on the distance between the point of force application and the axis of rotation?

I don't understand how the perpendicular distance between the point of force and the axis of rotation gets involved in the calculation of the rotational effect of that force.Is it about rotational ...