Help understanding centrefugal force

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In summary, Centrefugal force is a fictitious force that appears to act on objects in circular motion due to their inertia. It works by pulling objects away from the center of rotation and towards the outer edge of the circular path. It is often confused with centripetal force, which is the real force that keeps objects in circular motion. Centrefugal force has various applications in real life, such as in amusement park rides and scientific experiments. It can be calculated using the formula F = mv^2/r, which shows that it increases with mass, velocity, and the size of the circular path.
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Homework Statement



Basically i have to prove a lagrange equation using a non-inertial reference frame. A bead on a hoop where the hoop rotates as in the image below.
mN8wY.png


F = Fg + Fcf

Homework Equations



mR(d2θ/dt2) = mΩ2Rcosθsinθ -mgsinθ

what I'm supposed to get

The Attempt at a Solution



Fg = -mgsinθ

Fcf = m(ΩxR)xΩ = mΩ2Rcosθsinθ

I know that

Ω = Ω(0 , sinθ, cosθ)

R = R( 0 , k I'm just lost and frustrated :(
 
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This is probably late but does this work?
 

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What is centrefugal force?

Centrefugal force is a fictitious force that appears to act on objects in circular motion. It is not a real force, but rather an apparent force caused by an object's inertia.

How does centrefugal force work?

Centrefugal force works by pulling objects away from the center of rotation and towards the outer edge of the circular path. This is due to the object's inertia, or tendency to continue moving in a straight line, even as the path curves.

What is the difference between centrefugal force and centripetal force?

Centrefugal force and centripetal force are often confused, but they are actually two different forces. Centripetal force is the real force that keeps an object in circular motion, while centrefugal force is the apparent force that seems to pull objects away from the center of rotation.

How is centrefugal force used in real life?

Centrefugal force is used in many applications, such as amusement park rides, centrifuges in laboratories, and even in sports like figure skating and roller skating. It is also a key concept in understanding the rotation of planets and other celestial bodies.

How can I calculate centrefugal force?

Centrefugal force can be calculated using the formula F = mv^2/r, where F is the centrefugal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path. This formula shows that centrefugal force increases with mass, velocity, and the size of the circular path.

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