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

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How to find angular velocity of a point inner a circumference

Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
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47k 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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187 views

Appearing To Reverse Object's Rotation

Can it be done, and if so, how does one you explain mathematically the ability to cause a rotating object to appear to change the direction of rotation? I believe it has something to do with angular ...
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683 views

Vector Nature Of Angular Velocity

I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
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1k 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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1answer
307 views

Finding Max Radius of Propeller (angular velocity)

I am looking at a question from University Physics The given answer Whats the intuition behind using the below diagram of finding $v_{tip}$? I was looking the the $v_{tan}$ not knowing how ...
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181 views

Time for a wind-battred door to slam

Foolishly leaving the window too widely open, earlier today my bathroom door slammed shut with the wind. How could I theoretically work out the time it takes to close? Would it be impossible to ...
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1answer
515 views

what happens when I roll a gyroscope along its axis of spin

Say: I have a gyroscope that is spinning in the xy plane along the z axis. I then roll its spinning axis by some angle theta Now I know the gyroscope will resist my attempting to change its axis ...
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634 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 ...
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871 views

Meaning of angular velocity in a rotating system

When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
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1answer
503 views

Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...
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308 views

What conditions must be met for a ball to roll perfectly down an incline without slipping?

What conditions must be met for a ball to roll perfectly down an incline without slipping? A mathematically rigorous definition, please. I honestly don't know where to begin with answering this ...
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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 ...
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289 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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274 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 calclute the Angular velocity (w) of the two girls. So I set the ...
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873 views

What are the expressions for rotational and translational kinetic energies of a system of point particles?

Consider a system of point particles , where the mass of particle $i$ is $\mu_i$ and its position vector is $r_i$. What are the expressions for translational kinetic energy and rotational kinetic ...
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2k 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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2answers
370 views

Finding work done by rotational force?

A disk with a rotational inertia of 5.0 kg·m2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the ...
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812 views

Simple Harmonic Motion Question [closed]

I have two formulae: Displacement = Amplitude * Cos(Angular Frequency * Time) Velocity = - Amplitude * Angular Frequency * Sin(Angular Frequency * Time) OR $x = Acos(wt)$ $v = -A.w.sin(wt)$ And ...
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453 views

Equation that tells me the rpm and mass of a spinning disk needed to keep a second large mass stable using gyroscopic effects

I am trying to figure out how large of a mass and how quickly I need to spin said mass to keep a two-wheeled robot stable. Ideally, I am looking for a formula that relates m1=mass of robot, m2=mass of ...
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1k views

Tennis serving machine— How does a spinning ball bounce?

I have an idea of making a tennis serving machine. I will briefly describe what it is: The machine is configured to serve the ball at a fixed speed to the center of the left (or right) service court ...
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1answer
3k views

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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Dynamics of moment of inertia

I'd like to be able to determine the angular acceleration of a system of two rotating masses, which are connected so as to have a variable mechanical advantage between the two. My background with ...