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

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5answers
1k 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 ...
1
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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 ...
1
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0answers
28 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 ...
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 ...
0
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1answer
39 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 - ...
0
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1answer
155 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 ...
6
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1answer
4k views
0
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0answers
31 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 ...
2
votes
1answer
175 views

Kinematics of Euler angles relative to a rotating frame

I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and ...
0
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0answers
32 views

Unit ball rolling in a straight line on a flat plane, angular velocity as measured in a frame attached to the center of the ball

Suppose I have a unit ball rolling in a straight line at a constant velocity on a plane. There is a 3-axis inertial measurement unit (IMU) embedded in the ball at the center (so the ball has an ...
1
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1answer
57 views

How would the angular velocity of the rod change if it slipped on the table?

I wanted to consider a second case of my homework assignment. We were asked to solve the question: A uniform rod of length b stands vertically upright on a horizontal plane in a position of unstable ...
10
votes
2answers
2k views

Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
1
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0answers
19 views

integrating small angular velocities

I know that for a constant angular velocity the following is true: $R=e^{W t} R_0$ where $W$ is an angular velocity tensor, $t$ is a time, and $R$ is a rotation matrix I believe the following is ...
0
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2answers
90 views

Spinning an object in vertical circle

The situation : A block of mass $M$ is tied to a string and is spun around in a vertical circle. The question asks me to calculate the tension in the string 'at the lowest point' after giving ...
-1
votes
3answers
19k 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 ...
-1
votes
2answers
56 views

Shouldn't the net acceleration in circular motion always be zero?

I just learned the derivation of the acceleration vector in circular motion. I know that acceleration vector has two components which are centripetal acceleration($\omega^2ra_r$) and tangential ...
1
vote
2answers
16k views

Difference between angular frequency and angular velocity?

What is the difference between angular frequency and angular velocity? I think one is used for SHM and the other for circular motion? Also can both be used for centreptal accelartion? I think angular ...
0
votes
1answer
60 views

Why the point right below the center of a rolling ball on the ball has zero instantaneous velocity [duplicate]

Suppose there is a snooker ball rolling on a table. The velocity of the center of the ball is Rω and its direction is horizontally right. I don't understand why the point right below the center on the ...
2
votes
2answers
188 views

How many hours will be in a day if the radius of Earth increases by 70 m? [closed]

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
2
votes
1answer
222 views

A question on deriving a formula for a rotational object

I have this question assigned, but I really am stuck on how to do it: A bullet is shot through two cardboard disks attached a distance $D$ apart to a shaft turning with a rotational period $T$, as ...
3
votes
2answers
749 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 ...
1
vote
1answer
72 views

How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center)

A particle is revolving in horizontal a circle of radius $R$ with constant speed of $|\vec{v}|$ and constant angular velocity $\omega$. There is another observer standing inside the circle, at a ...
0
votes
2answers
94 views

Why isn't angular velocity the moment of velocity if angular momentum is moment of momentum? [closed]

Angular momentum can be defined as $L$ = $\textbf{r}$ x $m\textbf{v}$. Why is angular velocity $\omega$ then not $\textbf{r}$ x $\textbf{v}$, but instead $v = \omega \times \textbf{r}$?
2
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2answers
88 views

Can a GPS system detect the decline in the rotational velocity of the Earth?

From Wikipedia: Rotation in Angular Velocity of Earth Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's ...
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2answers
196 views

Is $v$ not always equal to $\omega r$ in angular motion?

NB:I am not asking an answer for the question quoted. I had this question given in my book: A ring of radius $R$ rolls on a horizontal ground with linear speed $v$ and angular speed $\omega ...
3
votes
3answers
9k views

Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion

The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is ...
0
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1answer
119 views

How to calculate the “angular braking distance” when you know the following values?

I have to calculate the arc length in radians that a circle spinning at speed will travel when it decelerates to $0$. I have the initial angular velocity in rad/s, the radius in meters, the mass in ...
5
votes
3answers
861 views

How can I relate linear and angular motion using a single formula?

I want to relate linear and angular motion using a single formula. Assume I have a 10m rod, and I apply a force of 5N on it, 2.5m away from the axis of rotation for 1s. How can I determine the ...
2
votes
3answers
23k 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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vote
5answers
220 views

Why does solving $\mu mg = m \frac{v^2}{r}$ give the *max* possible velocity?

So here is the standard problem setup of a car turning on an unbanked road: A 1000 kg car is going around a curve with radius 30 meters. If the coefficient of friction between the car's tires ...
1
vote
1answer
262 views

How much does air resistance affect the angular velocity of a golf ball?

I'm modeling the flight trajectory of a golf ball, and using angular velocity to calculate the Magnus force. Currently, I'm assuming angular velocity to be fixed throughout the ball's flight. How ...
4
votes
2answers
164 views

Intuitive explanation for why centripetal acceleration is $\frac{v^2}{r}$

There are several ways to write centripetal acceleration $$\frac{v^2}{r} = \omega^2 r = v \omega$$ Are there intuitive explanations for any of these three forms? For instance, I can sort of explain ...
0
votes
1answer
63 views

Moving objects along a radius

I'm working on a project involving a Roomba which I'd like to move precisely from coordinate to coordinate. To move the Roomba manually you need to give it a velocity between -500 to 500mm/s and a ...
4
votes
3answers
9k 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 ...
0
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0answers
51 views

Need clarification for Relation between angular momentum and centripetal force

I've recently started studying angular momentum, so, as far as I understand, angular momentum is conserved as long as any form of centripetal force can be maintained in the new system or otherwise it ...
0
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0answers
23 views

Can't we assign any other direction for instantaneous angular velocity except along the axis of rotation? [duplicate]

We specify the direction of instantaneous angular velocity using the right hand thumb rule. I just want to know that is it just a matter of convention or we don't have any other direction for it to be ...
2
votes
2answers
545 views

In which direction does mud fly off a moving bike's tire & why?

If a bike moves through a muddy area, mud gets on its tires. Then the mud flies off from the tires. Which forces are acting on it? In which direction does it fly off? On my physics test, I wrote ...
3
votes
1answer
84 views

Why do you seem to go faster as you hug a turn?

I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, ...
0
votes
2answers
152 views

When does the 'standard' angular velocity formula not hold?

I have read that the formula for angular velocity: $$\dot {\vec r}=\vec \omega \times\vec r \tag{1}$$ does not hold in some situations, but the book does not specify what situation so please could you ...
2
votes
1answer
90 views

If $\omega = \frac{v}{r}$, why do we need torque?

If $\omega = \frac{v}{r}$, then why do we need torque and angular acceleration? The velocity v can be found just by Newton's second law of motion $F = ma => a = F/m$ and $v = v_0 + at$ . Then we ...
1
vote
1answer
63 views

Force responsible for increasing a spiraling object's tangential velocity

Suppose we have a small mass attached to a string that has been fed through a hole in the friction-less table on which the mass is rotating. Pulling the string downwards thus decreases the radius of ...
1
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1answer
162 views

Movement and Rotation of a Inverted-Pendulum-like Object with External Forces

I'm struggling to model the movement of a complex object based on an external force. Let's start with a simple example of what I'm looking for. We have a block $b$ of mass $M_b$, moving ...
0
votes
1answer
189 views

Calculating the charge of weights on a rod based on it's movement in an electric field

I've got a problem from my physics course which I am a little stuck on. A dumbell consisting of two identical masses m=5.8 kg attached to the ends of a thin (massless) rod of length a=0.4 m that ...
6
votes
1answer
3k 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 ...
0
votes
1answer
54 views

Angular velocity in central force field

For motion in a central force field consider a rotating reference frame, which is characterized by the Euler angles $\alpha$, $\beta$, $\gamma$ associated with the rotation of the frame of Cartesian ...
1
vote
1answer
156 views

What causes angular and linear deceleration in a sliding and rotating ring?

I was solving an AP Physics problem involving a ring sliding and rotating over a frictional surface. When I started to think about why the ring eventually comes to a stop I started to become confused. ...
1
vote
1answer
173 views

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

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 ...
3
votes
3answers
117 views

Why is acceleration significant to generating power in racket sports?

I'm reading a paper on badminton stroke power (see Figure 4 on page 8). It says: For most of the trials the racket head reached peak speed just at the time of impact. The racket head showed ...
3
votes
4answers
373 views

How can I measure the speed of a figure skater's spin?

My daughter is a figure skater and needs to measure how fast she is spinning before she loses her position. This is a science project for 7th grade. I have looked for devices to possibly measure her ...