The sagging effect and angular speed.

[alevis]

Homework Statement

Does anyone know anything about the sagging effect of a object with mass m rotating in a circular path at an anle of "theta" below the horrizontal?
How do you find the theoretical angular speed the the object is rotating at R revs/d in t seconds at an angle of "theta" degrees (because of sagging effect caused by gravity). You are given the angular speed in revs/s, the time in t seconds and the force of gravity acting on the object during it's motion but not the angle below the horrizontal. How do you find it.
I'd also like to know how the sagging effect affects the theoretical angular speed.
I would like to know how to find the rea

Homework Equations

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The Attempt at a Solution

None.

 

[Imperitor]

As the object travels downward the potential energy it had is converted to velocity. This is why the object will speed up at the bottom and slow down at the top.

Basically you take the change in height of the object, figure out how much potential energy was converted to kinetic energy over that height and then convert that velocity from m/s to rad/s.

 

[nlightner]

I am happy to provide some information on the sagging effect and angular speed. The sagging effect, also known as the centrifugal force, is the apparent outward force experienced by an object rotating in a circular path. This is caused by the object's inertia trying to keep it moving in a straight line, while the circular motion pulls it towards the center.

To find the theoretical angular speed of an object rotating at an angle of "theta" degrees, we can use the equation ω = v/r, where ω is the angular speed, v is the linear speed of the object, and r is the radius of the circular path. In this case, the linear speed (v) can be found using the equation v = ωr, where ω is the angular speed and r is the radius.

The sagging effect caused by gravity will affect the theoretical angular speed by slightly increasing it. This is because gravity adds an additional force pulling the object towards the center of the circle, causing it to travel at a slightly higher speed. However, the effect of gravity on the theoretical angular speed is usually very small and can be neglected in most cases.

To find the angle below the horizontal at which the object is rotating, we can use the equation tanθ = v/g, where θ is the angle, v is the linear speed of the object, and g is the force of gravity. This equation can be rearranged to solve for θ, giving us θ = tan^-1(v/g).

I hope this information helps you understand the relationship between the sagging effect and angular speed. If you have any further questions, please feel free to ask.