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

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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
165 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
268 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
174 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
58 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
277 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
364 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
325 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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1answer
2k views
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2answers
464 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
372 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
2k 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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0answers
72 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
509 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
593 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
140 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
1
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1answer
91 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
9k 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 ...
2
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0answers
116 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
360 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 ...
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0answers
42 views

How to get from angular velocity to acquired phase for neutrino oscillations in matter?

I am reading Akhmedovs 2000 paper on parametric resonance, and I cannot figure out the math of this particular passage: The difference of the neutrino eigenenergies in a matter of density $N_i$ is ...
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1answer
2k views

Drag on a spinning ball in fluid

I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I ...
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2answers
429 views

Lagrange-Euler equations for a bead moving on a ring

A bead with mass $m$ is free to glide on a ring that rotates about an axis with constant angular velocity. Form the Lagrange-Euler equations for the movement of the bead. Solution: Let us ...
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0answers
82 views

Truck driven from a small motor that can carry a heavy load, yet can travel fast.

I am building a truck from trash as materials. I have one small motor and a a few small gears, but no other engineered materials are allowed. The truck must carry a load for a distance of 3m. The ...
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1answer
1k views

Does weight distribution affect angular velocity?

If an equal torque of equal radius and size is produced on two bodies of the same weight and same center of gravity, but with different weight distribution (say one has a 1kg mass 1 meter above the ...
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0answers
337 views

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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3answers
61k 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
225 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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2answers
893 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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2answers
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 ...
2
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1answer
443 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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1answer
197 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 ...
3
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1answer
706 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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2answers
831 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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2answers
1k 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 ...
3
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1answer
607 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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1answer
372 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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3answers
1k 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
3k 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
437 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 ...
0
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1answer
993 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 ...
3
votes
1answer
508 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 ...
0
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1answer
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 ...
13
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1answer
4k 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 ...
3
votes
2answers
1k views

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 ...