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

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Need help understanding angular acceleration due to gravity

The question asks what the angular acceleration of an uniform disc of radius $R$ rotating about an axis passing through its edge if it is released from rest with its center of mass at the same height ...
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78 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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61 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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348 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
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27 views

Finding Angular Speed Problem [closed]

A cylinder of mass 5.0 kg and radius 0.20 m is attached to an axle parallel to its axis and through its centre of mass. A constant force of 6.5 N acts on the cylinder. Find the angular speed of the ...
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69 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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35 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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48 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
18 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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578 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
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1answer
373 views

Magnitude of the average velocity vector (not the average speed)

Thank you ahead of time for taking to look at this. For this following problem we were given an answer however I am almost positive the given answer is wrong. It doesn't even make sense. So here is ...
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2answers
213 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why? Please try to give a different explanation ...
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34 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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21 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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34 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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2answers
4k 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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1answer
257 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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1answer
31 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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29 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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32 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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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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Home experiments to measure the RPM of a pedestal fan without special equipment?

Is it possible to determine to an approximate degree, the revolutions per minute of a fan, for example a pedesal fan pictured below, without using some electronic/mechanical measuring device? One ...
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49 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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42 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
507 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
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1answer
40 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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23 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
23 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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98k views

Linear acceleration vs angular acceleration equation

I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration ...
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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
50 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
105 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
35 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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78 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
125 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 ...
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2answers
27 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
57 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
43 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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3answers
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How long was a day at the creation of Earth?

Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)? I ...
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911 views

Time derivative of angular velocity in rotating reference frame

I am going through a section in a textbook regarding the Newton Euler equations for a system of rigid bodies (robotics text). There is a particular line in the derivation I don't understand, I've ...
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2answers
69 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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48 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
143 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
282 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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1answer
96 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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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 ...
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1answer
57 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
28 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 ...
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2answers
88 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 ...