Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [circular-motion]

For questions related to circular motion (movement of an object along the circumference of a circle or rotation along a circular path).

(In physics) Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a $3$D body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same.

For the various equations and formulas on the same, check this link.

26 questions
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Motion in a vertical circle (Mechanics / Physics) solution error?

I wonder if someone would be kind enough to check a solution that I feel contains an error? Question A small bead, of mass $m$, is threaded on a smooth circular wire, with centre $O$ and radius $a$, which is fixed in a vertical plane. You may…
Dave M
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Obtain gravity direction by observing a pendulum's movement

Lets say a damped pendulum takes 10 seconds to slow down and stop. In that time it might swing past vertical perhaps 25 times or so. We have an accurate clock that measures absolute time reliably. We are given very accurate speed and direction…
Wossname
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A doubt on polar coordinates in the plane

I'm here to ask a really stupid question just to be sure of its answer. My professor gave us an exercise where we have to determine the Lagrangian of a system that is formed by a circular ring of mass $M$ and radius $R$ which is placed in the…
deomanu01
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Circular random walk coupon collector's problem for large numbers of coupons

I need to know if there is a formula or asymptotic approximation for the following coupon collector's problem involving very large numbers of coupons. Coupons are arranged in a circle It doesn't matter which coupon is collected first Coupon…
user14343099
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Uniform Horizontal circular motion of a car on a banked slope with friction.

I came up with this question, to try to help my understanding with uniform circular motion of an object on a banked slope: A car moving with speed $144$kmh$^{-1}$ is on a banked inward slope, the slope has angle $\theta^{\circ}$ to the horizontal.…
Adam Rubinson
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If a point is situated on a circle and the circle rotates 180 degrees to the right, what would be the total displacement of the point?

I have a point $P$ situated on the circumference of a circle with radius $r=2$ (as shown here) and the circle rotates along the x-axis by $180^°$ to the right. If the circle rotates by that amount, it should travel $2\pi$ units (half its…
Noor
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How to find the intersection of a pair of equal arcs arcs touching two points

Though this question doesn't have mathematical origins, it boils down to geometry. I'm a high school student so forgive me if the answer is obvious, I will likely have overlooked it. I am building a robot which is controlled like a tank, with one…
user17301834
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What is the most efficient way to cover (not literally cover) a circular area?

All of the questions I found are about literally covering "What is the most effective way to cover a circular pot with a square lid etc..." Here's an example to show what I mean: I have a circular farm of 10,000 sq m in area. I have a crop duster…
Walt
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Prove that the trajectory of $P$ is a circle in $3D$ and find its properties

A point $P=(x,y,z)$ starts off at $P(0)= (x_0, y_0, z_0)$. Its time derivative is given by $ \dfrac{d P}{dt} = a \times P $ where $a \in \mathbb{R}^3$ a unit vector, and $\times$ is the cross product. Show that the trajectory $P(t)$ is a circle;…
user948761
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Integrating $\int \frac{d\theta}{\sqrt{a-b \sin \theta}}$

I was looking into rotational motion in physics and encountered this integral where a and b are constants. $$\int\frac{d\theta}{\sqrt{a-b \sin \theta}}$$ I have found that it looks like an elliptic integral, but I am not familiar with them. How…
user1244595
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Stopping distance for object moving in a circle

An object is moving in a circular path of radius $r$. It has a linear (tangential) velocity $v$. The linear (tangential) deceleration of the object is $d$. In other words, d is the rate of decrease of $v$. How can I calculate its stopping distance…
simplename
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When does the rotating wall hit the pole?

The circle's circumference is $c$ meters, and it rotates at a speed of $v$ RPM. The hole in the circle has a breadth of $l$ meters, and the pole (colored black) has a diameter of $d$ meters. The pole is in the center of the hole. When will the…
user110391
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Constant angular acceleration suvat-related equations: OCR Further Maths A Level "Focus on Proof" page $130$

Angular displacement is represented by the symbol $\theta.$ Angular velocity is the rate of change of angle and is denoted by $\omega$ or $\overset{.}{\theta}. $ Angular acceleration, which is the rate of change of angular velocity, is denoted by…
Adam Rubinson
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Circular Motion of speedboat towing water skier

I'm confused about the following simple circular motion question. A water skier of mass 100 kg is being towed by a speed boat, the length of the tow rope being 30 meters. Boat and skier are moving with constant speed in concentric circles of radii…
Stephan
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How to write a constant turn motion model for multiple objects(>2)?

I am working on multiple object tracking. The next state of a state variable given the current state is characterized by the equation $x(k+1) = Fx(k) + noise$. $F$ is a state motion model matrix. It models the motion of state variable $x$. For a…
sandeep chinthala
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