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

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The Linear acceleration in Gyroscope

I am trying to understand theory behind the Gyroscope. I found this article that explains things in much detail. But I am unable to understand how that perpendicular acceleration components (a1, a2) ...
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1answer
706 views

What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
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90 views

Examples of projection of angular velocity

I am looking for examples where the projection of angular velocity vector onto a different axis, has some interesting physical meaning in day-to-day contexts. For example, if a gramophone turntable ...
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1answer
88 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 ...
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2answers
77 views

Having trouble understanding how the centrifugal force works

I thought that I understood the centrifugal force earlier, but I can't seem to grasp how it interacts when considering that everything is relative? Let's imagine that you are the only one in the ...
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2answers
2k views

Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
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2answers
218 views

How do you travel in a circular orbit around a massive body?

I am trying to figure out how an object could achieve a perfectly circular orbit. Given a mass for the planet or other body the object is orbiting and a distance from the center of mass, how fast ...
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1answer
79 views

Have I calculated Angular Acceleration correctly?

I am teaching myself basic mechanics from a standing start. I am trying to understand Angular Acceleration and have set myself a problem to solve. My answer 'feels' wrong, so I'd like some help to ...
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1answer
76 views

How do I calculate the necessary velocity of two reels of tape to maintain constant tension on the tape?

I have a real-world problem that I'm quite certain can be solved with a formula. Unfortunately I myself am not particularly skilled in the realm of physics or math. Any and all help is very much ...
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1answer
385 views

Angular velocity $\omega$ by $v$

We have two girls, with mass ($M$). They become close to each other in speed of $V$. The distance between them is $3L$. I was asked to calculate the Angular velocity ($\omega$) of the two girls. So ...
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2answers
348 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
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3answers
94 views

How can I compute the angular velocity of a triangle formed by three particles knowing their instantaneous positions and velocities? [closed]

I have a set of trajectories of three particles and their instantaneous velocities. I would like to compute the 3 components of the angular velocity pseudovector of the fictive triangle formed by ...
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1answer
447 views

Finding stopping time when only given initial angular velocity and an expression for angular acceleration?

Question: A wheel starts is spinning at $27\text{ rad/s}$ but is slowing with an angular acceleration that has a magnitude given by $\alpha(t) = (3.0\;\mathrm{rad/s^4})t^2$. It stops in a time ...
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1answer
74 views

Angular velocity vector in terms of motion of an object

May be it is small question in this forum but I'm trying to get the feel of the understanding about the angular velocity. If this question is getting rejected please kindly refer me to appropriate ...
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0answers
80 views

Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
3
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1answer
71 views

Will a rotating body gain linear acceleration in water?

If a ball is floating in water and it has some angular velocity, will it gain some linear acceleration from the drag on it as it rotates? Edit: This is how I pictured it. I guess my reasoning is ...
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2answers
922 views

Relative angular velocity and acceleration

Background: (Irodov 1.55) Two bodies rotate around intersecting perpendicular axes with angular velocities $\hat\omega_1,\hat\omega_2$. Relative to one body, what is the angular-velocity and ...
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2answers
7k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
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1answer
179 views

How do I find angular and linear velocity after normal force and “infinite” friction force?

Look at this picture: http://i.imgur.com/mY8ShkV.png Here we have a ball resting on top of a platform (the contact point is marked red). I know the normal vector (marked green). I also know the mass, ...
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1answer
113 views

Why is it that angular acceleration is constant in different instantaneous reference frames?

Take the following example: A rod (of length L and mass m) is held horizontally at both ends by supports. One is instantaneously removed. The specific problem is to prove that the force on the other ...
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110 views

Rolling in 3D using Torque, Angular Momentum/Velocity

I'm stuggling to get a simulation working correctly. Below you can see what I am attempting to do. You can also view it here. Can you spot where I'm going wrong? (Calculated at start) 1) Inertia ...
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1answer
697 views

How do I convert tangential speed to angular speed in an elliptic orbit?

I am running an animation of a satellite in an elliptic orbit (defined by a parametric equation for $x$ and $y$ as a function of $t$) and want to make sure the spacecraft is traveling at the right ...
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2answers
166 views

Does an object on top of a lever arm have angular velocity at the moment when the lever is released?

Suppose there is a lever arm fixed at one end, and it is parallel to the ground. There is an object resting somewhere on top of the lever arm (the object is not attached to the lever). At the moment ...
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1answer
96 views

Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...
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1answer
311 views

Why is body frame angular velocity nonzero?

This question is relevant to Euler's angles and Euler's equations for a rigid body. Why aren't $\omega_1$, $\omega_2$ and $\omega_3 = 0$ in the body frame? How can we measure $\vec\omega$?
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1answer
147 views

Paradox of angular velocity

For a torque-free symmetric top, the Inertia tensor has an inverse $I^{-1}$, and $L=I\omega$. Which implies that $\omega=I^{-1}L$. But since $I, L$ are constants, $\vec\omega$ is a constant. However, ...
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1answer
563 views

Rod slipping against block due to gravity? [closed]

A uniform rod of mass $m$ and length $l$ is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a ...
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1answer
160 views

Does angular momentum conservation imply that angular momentum $J$ is parallel to angular velocity $\omega$?

In other words, does $\frac{dJ}{dt} =0$ imply $J \times \omega =0$? Counterexamples or proofs would be helpful! EDIT: This question originally asked if $\frac{dJ}{dt} =0 \Leftrightarrow J \times ...
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2answers
15k 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 ...
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2answers
173 views

Not so simple problem using momentum, energy and angular velocity…?

I have an object in free space (no gravity) with angular momentum $ = \omega_i $, and some velocity vector $=\vec{V_i}$. To simplify we will say it has a mass-less rigid rod length $ = \ell $, ...
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2answers
353 views

Angular position vector?

I'm a mathematician, so I like my angular velocities to be vectors. It makes my angular momenta and torques vectors as well, and so they have nice operations I can do on them. Because of that, I pick ...
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2answers
208 views

How does the curve ball drag air around it?

In cricket or baseball there is a type of ball called the curve ball. This is the top spin of the ball.I read that due to spin the ball drags the air around it due to friction in the way shown ...
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1answer
62 views

Can we define angular momentum for the wheel under motion?

According to the definition of angular momentum: Angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and ...
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1answer
459 views

Reference Frame and Angular Speed Related?

I am given the following problem: If an airplane propeller rotates at 2000 rev/min while the airplane flies at a speed of 480 km/h relative to the ground, what is the linear speed of a point on ...
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1answer
424 views

How do the units for angular velocity come out of $\omega = \sqrt{k/m}$?

I'm confused about an exercise of a book. I understand that the units for angular velocity is $\text{rad/s}$; but I don't understand, how can I get it from the relation $\omega=\sqrt{k/m}$. Solving ...
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1answer
393 views

Canonical momentum Velocity dependent Lagrangian

I have a homework problem wich I think I'm on the verge of solving but need help with some relations: Show that if the potential $U$ in the Lagrangian contains velocity-dependent terms, the ...
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2answers
530 views

What are the consequences of relativistic angular velocities?

If I take a rod of some radius $r$ and length $L$, and I spin this rod with angular velocity $\omega$. How would the geometry of the rod appear to an observer as one converges to $c$? What are the ...
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1answer
463 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
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3answers
3k views

Time period of torsion oscillation

For the oscillation of a torsion pendulum (a mechanical motion), the time period is given by $T=2\pi\sqrt{\frac{I}{C}}$ which is a result of the angular acceleration ...
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78 views

Observed angular velocity and motion parallax

I would be highly obliged if someone would guide me in the right direction regarding this. I am trying to understand and mathematically explain the relation between angular velocities as observed by ...
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0answers
94 views

Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...
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2answers
586 views

Moment of inertia of a football and its angular momentum

What are the ways to create a mathematical model for the moment of inertia of a football? Can the moment of inertia of the football be simplified to two cones stack against each other? I'm trying to ...
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1answer
724 views

Component of angular velocity along an axis inclined at $\theta$

If an arbitrary rigid body rotates with angular velocity $\omega_0$ about some axis, can it be said that the body will rotate with an angular velocity $\omega_0 \cos(\theta)$ about an axis which is at ...
3
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1answer
156 views

Two masses on rope spinning around

Two balls of the same mass $m$ are connected to each other with rope of length $l$. One of the balls is also connected to the ceiling with a rope of the same length $l$. The balls are spinning ...
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2answers
2k views

Slowdown rate of rotating body due to friction force [closed]

This isn't a homework question, but it might as well be. The problem I have been pondering is: If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
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5answers
2k views
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1answer
105 views

Determine the velocity and acceleration of the vertex $B$

1) The bent rod $ABCD$ rotates about the line $AD$ whit a constant angular velocity of $90 rad / s$. Determine the velocity and acceleration of the vertex $B$ when the rod is in the position shown in ...
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3answers
12k views

Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
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121 views

Closed-form equation for orientation and angular velocity over time

If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
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1answer
418 views

Circular motion and centrifugal force

Assuming a race car drives around in a circle of radius r, center (0,0), linear velocity v, and ignoring centrifugal forces and friction I can calculate the position at any time, t. Angular velocity ...