Tagged Questions

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

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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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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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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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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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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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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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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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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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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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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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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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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 $... 1answer 30 views Why does a ball rotate sometimes when you throw it? My guess is that when you throw a ball, which is held by your hand, using you arm, the radius of the circular path being constant, the outermost part of the ball has a bigger radius than the innermost ... 2answers 123 views angular velocity of rigid body I am doing some physics for a game. I have a rigid body defined as multiple balls of the same mass distributed to make some object. Let's say I put to each ball a different velocity but because it is ... 5answers 2k views motion in the body-fixed frame? This is really basic, I'm sure: For rigid body motion, Euler's equations refer to$L_i$and$\omega_i$as measured in the fixed-body frame. But that frame is just that: fixed in the body. So how ... 3answers 73 views Angular velocity from orientational displacement A 3-dimensional object is rotating around an unknown 3-dimensional axis through the object's center of mass. Its orientation is described by two unit vectors. I know an initial orientation and a final ... 0answers 30 views Total angular velocity (Kerr metric) I have a problem with the kerr metric and the "rotating spacetime" in the ergosphere. How can i calculate the angular velocity$\omega$of an object in the ergosphere (which flys from infinity into ... 1answer 16 views Which part of an angular velocity vector is its direction? I am assuming that an angular velocity vector only has two direction: positive for counterclockwise and negative for clockwise. Just to make sure that I have the right interpretation. Newton's 1st ... 1answer 40 views Direction of angular velocity please help me here! Im confused, is direction of angular velocity perpendicular to the plane of motion, or along the plane of motion?? From hyperphysics - http://hyperphysics.phy-astr.gsu.edu/... 1answer 195 views How do you calculate theoretical ratios of angular velocity final and angular velocity initial? [closed] I'm asked to calculate the "Theoretical Ratio". ($\omega_f/\omega_i$) I have Inertia of the Disk =$I_{DISK} = .0094115713$, I have Hoop Inner Radius =$I_R = 55.725$So I am supposed to use the ... 1answer 4k views Example where angular momentum and angular velocity are not parallel I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel. 0answers 33 views How rotational force calculation depends on the distance between the point of force application and the axis of rotation? I don't understand how the perpendicular distance between the point of force and the axis of rotation gets involved in the calculation of the rotational effect of that force.Is it about rotational ... 1answer 181 views Kinematics of Euler angles relative to a rotating frame I have a rotating body$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$and$\omega_F$.... 0answers 34 views Unit ball rolling in a straight line on a flat plane, angular velocity as measured in a frame attached to the center of the ball Suppose I have a unit ball rolling in a straight line at a constant velocity on a plane. There is a 3-axis inertial measurement unit (IMU) embedded in the ball at the center (so the ball has an ... 1answer 59 views How would the angular velocity of the rod change if it slipped on the table? I wanted to consider a second case of my homework assignment. We were asked to solve the question: A uniform rod of length b stands vertically upright on a horizontal plane in a position of unstable ... 2answers 3k views Dynamics of counter-rotating flywheels I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ... 0answers 20 views integrating small angular velocities I know that for a constant angular velocity the following is true:$R=e^{W t} R_0$where$W$is an angular velocity tensor,$t$is a time, and$R$is a rotation matrix I believe the following is ... 2answers 96 views Spinning an object in vertical circle The situation : A block of mass$M$is tied to a string and is spun around in a vertical circle. The question asks me to calculate the tension in the string 'at the lowest point' after giving ... 3answers 20k views Finding Angular Acceleration of rod given radius and angle A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ... 2answers 61 views Shouldn't the net acceleration in circular motion always be zero? I just learned the derivation of the acceleration vector in circular motion. I know that acceleration vector has two components which are centripetal acceleration($\omega^2ra_r$) and tangential ... 2answers 17k views Difference between angular frequency and angular velocity? What is the difference between angular frequency and angular velocity? I think one is used for SHM and the other for circular motion? Also can both be used for centreptal accelartion? I think angular ... 1answer 60 views Why the point right below the center of a rolling ball on the ball has zero instantaneous velocity [duplicate] Suppose there is a snooker ball rolling on a table. The velocity of the center of the ball is Rω and its direction is horizontally right. I don't understand why the point right below the center on the ... 2answers 189 views How many hours will be in a day if the radius of Earth increases by 70 m? [closed] I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ... 1answer 243 views A question on deriving a formula for a rotational object I have this question assigned, but I really am stuck on how to do it: A bullet is shot through two cardboard disks attached a distance$D$apart to a shaft turning with a rotational period$T$, as ... 2answers 777 views Ten-ping bowling: Can a ping pong ball knock over a bowling pin? In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ... 1answer 77 views How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center) A particle is revolving in horizontal a circle of radius$R$with constant speed of$|\vec{v}|$and constant angular velocity$\omega$. There is another observer standing inside the circle, at a ... 2answers 94 views Why isn't angular velocity the moment of velocity if angular momentum is moment of momentum? [closed] Angular momentum can be defined as$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}$? 2answers 89 views Can a GPS system detect the decline in the rotational velocity of the Earth? From Wikipedia: Rotation in Angular Velocity of Earth Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's ... 2answers 232 views Is$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 =2v/R$... 3answers 9k views Proof of centripetal acceleration formula ($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 ... 1answer 157 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 ... 3answers 884 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 ... 3answers 24k 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 ... 5answers 228 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 ... 1answer 337 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 ... 2answers 181 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 ...
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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 ...
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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 ...