# Analyzing Forces in Circular Motion: Finding Equilibrium in a Spring System

• LCSphysicist
In summary: What do you think will happen if the rod is rotated about its axis?I don't know how to put this in a system possible and determined, that is, obtain the answer only with the variables given.
LCSphysicist
Homework Statement
A device (Fig. 1.26) consists of a smooth L-shaped rod located in a horizontal plane and a sleeve A of mass m attached by a weightless spring to a point B. The spring stiffness is equal to x. The whole system rotates with a constant angular velocity co about a vertical axis passing through the point 0. Find the elongation of the spring. How is the result affected by the rotation direction?
Relevant Equations
N,
P = mg
F = minus kx
https://www.physicsforums.com/attachments/262043I got here, i think that the component y N will balance the mg force; the other componente of N will be divided in two, one to balance the force, and other to be the centripal result, but i don't know how relate to each other

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Since this is a rotational motion with constant speed, what can you say about the tangential and centripetal accelerations (and thus the forces)?

It would help if the figure showed points O, A and B mentioned in the statement of the problem. I can imagine the sleeve being the white cylinder labeled mg. Is the spring the black thing next to it? I would assume the axis of rotation is the black line on the left. If so, it is shown correctly parallel to the weight. Please show your attempt at this. When you do so and to avoid unnecessary confusion and utter chaos, please use ##k## not ##x## to denote the spring constant.

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nothing to understand

archaic said:
Since this is a rotational motion with constant speed, what can you say about the tangential and centripetal accelerations (and thus the forces)?
The tangencial force will cancel and the modulus of centripetal force will be constant since R is constant. ?
I don't know how to put this in a system possible and determined, that is, obtain the answer only with the variables given.

kuruman said:
It would help if the figure showed points O, A and B mentioned in the statement of the problem. I can imagine the sleeve being the white cylinder labeled mg. Is the spring the black thing next to it? I would assume the axis of rotation is the black line on the left. If so, it is shown correctly parallel to the weight. Please show your attempt at this. When you do so and to avoid unnecessary confusion and utter chaos, please use ##k## not ##x## to denote the spring constant.

I totally agree with you

The blue axis is where route around.

I call B the point where the spring is attached

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LCSphysicist said:
The text says the L is in a horizontal plane. If so, what has mg to do with it?
The diagram is a perspective drawing, yes? The angle in the rod is really a right angle and the axis of rotation and the weight mg are normal to the L.
r is the hypotenuse... it's not clear, but I would guess the arms of the L are equal in length.

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LCSphysicist said:
The tangencial force will cancel and the modulus of centripetal force will be constant since R is constant. ?
I don't know how to put this in a system possible and determined, that is, obtain the answer only with the variables given.
I totally agree with you

View attachment 262053The blue axis is where route around.

I call B the point where the spring is attached
How about drawing a free body diagram of the sleeve showing all the hotizontal forces acting on it?

kuruman said:
How about drawing a free body diagram of the sleeve showing all the hotizontal forces acting on it?
The problem is that just one force is on a horizontal, the elastic force. Look my justification:

Probably i am seeing wrong, this leave me to a lot components of N :|

Are you saying that the rod does not exert a horizontal force? It will if it is necessary that it does so. In what direction is the centripetal acceleration? Can the elastic force account for all it? Hint: If the sleeve were at the end of a rod shaped like an I not like an L, that would be the case.

LCSphysicist said:
The tangencial force will cancel and the modulus of centripetal force will be constant since R is constant. ?
I don't know how to put this in a system possible and determined, that is, obtain the answer only with the variables given.
I totally agree with you

View attachment 262053The blue axis is where route around.

I call B the point where the spring is attached
the tangential components should be along the line perpendicular to the radius. suppose that there is an angle between the radius and the rod and project your forces onto it.

## What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path, with a constant distance from a fixed point.

## What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain circular motion.

## What is the difference between centripetal force and centrifugal force?

Centripetal force is the inward force that keeps an object in circular motion, while centrifugal force is the outward force that appears to push an object away from the center of the circle. However, centrifugal force is actually just an apparent force and does not actually exist.

## What are some real-life examples of circular motion?

Some examples of circular motion include the motion of a car around a curved road, the motion of a satellite around a planet, and the motion of a spinning top.

## How does circular motion relate to Newton's laws of motion?

Circular motion relates to Newton's laws of motion in that the first law states that an object in motion will continue in a straight line at a constant velocity unless acted upon by an external force. In circular motion, the object is constantly changing direction, so there must be a force acting on it (centripetal force). The second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In circular motion, the acceleration is directed towards the center of the circle and is caused by the centripetal force. The third law states that for every action, there is an equal and opposite reaction. In circular motion, the centripetal force is countered by the centrifugal force, which is the reaction force.

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