# Circular Motion Problem (Using Newtonian Physics)

• Dougggggg
In summary, the problem is to find the time it takes for 1 revolution around a pole that is 3 meters long, with a 5 meter cable attached at an angle of 30 degrees from the vertical. The only other figure that can be solved for is just -g. The solution was found by breaking down the free body diagram of the seat, and solving for the centripetal acceleration. The answer was found to be 5.91 seconds.
Dougggggg

## Homework Statement

The problem is basically a fair ride that has a pole as its base, another pole sticking out of it, the a cable with a chair at the end. I am given the length of the rod sticking out (3.00 m), the cable (5.00 m) and the angle between 30.0$$\circ$$. I have to find the time it takes for 1 revolution around. The only other figure I can come up with is just -g.

## Homework Equations

$$\Sigma$$Fy=may=Fc-mgcos$$\theta$$=0
arad=$$\frac{v^2}{R}$$=$$\frac{4\pi^2}{T^2}$$

## The Attempt at a Solution

All I have done so far is solved for the how far the seat is from that 30 degree angle in both x and y directions. I had been flying through these problems except this one is like a wall, I have been lost on it for the past about 4 hours. Though my frustration and anger has made it difficult to make any progress. If anyone can point me in the right direction, I see nothing but dead ends no matter which way I try to solve this. I am going to try to rework my free body diagram, will edit when have more figured out.

Edit:Close thread, found out how to do this. Used some of forces equations to solve for m on both equations and then replaced my a with the second equation up there, my forces canceled, now just have some algebra to do.

Last edited:
Solve for centripetal acceleration.

MHrtz said:
Solve for centripetal acceleration.

I found out how to do it, I don't know if I could have solved for my centripetal acceleration since I have not been given any acceleration values other than gravitation. Maybe I am misunderstanding what you are telling me.

How did you find the answer and do you know if it's right?

I simply broke down my free body diagram of the seat and cam up with these equations.

$$\Sigma$$Fsy = may = Fccos$$\theta$$-mg = 0
$$\Sigma$$Fsx = max = Fcsin$$\theta$$

Then moved the mg over to that 0, divided by g to solve for m. Then solved for m on the bottom equation and substituted for the m in each equation to have.

(Fcsin$$\theta$$)/ax = (Fccos$$\theta$$)/g

Then I used the second formula in my original post to replace my ax with the second part of the arad equation. Then had a big mess, however, my Fc ended up canceling and my only unknown variable left is T which is what I need to solve for XD.

I think I had more trouble with this simply because I was stressing over things going on in my life, and thus made it difficult to focus. I still appreciate all the help that was offered.

The centripetal acceleration is ax^2 + ay^2 but you only needed the radial component ax. That's what I was getting at. Nonetheless, good work.

If anyone has completely worked this did you get an answer along the lines of 5.91 s? It is an even problem and my book only has odd answers in the back.

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path.

## 2. How is circular motion described using Newtonian physics?

In Newtonian physics, circular motion is described as the movement of an object with a constant speed, but changing direction at every point.

## 3. 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.

## 4. How is centripetal force related to circular motion?

Centripetal force is directly proportional to the mass and the square of the velocity of the object, and inversely proportional to the radius of the circle. This means that as any of these factors change, the centripetal force also changes, affecting the object's circular motion.

## 5. How is circular motion different from linear motion?

Circular motion involves an object moving along a circular path, whereas linear motion is the movement of an object in a straight line. In circular motion, the direction of the motion is constantly changing, while in linear motion, the direction remains constant.

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