Non-centered Rotating Arm with Hinged Weight

[DrTuring]

Homework Statement

I have a an arm with an attached hinge and weight that is rotating inside of a circle, but important the arm is not rotating about the center of the circle. The arm is spinning fast enough so that the weight is always making contact with the edge of the circle. I need to calculate the force applied against the circle by the weight for any given arm rotation.

Homework Equations

F = m*(v^2)/r

but I'm really confused about whether r should be the distance to the rotation point or the distance to the center of the circular path the weight is following.

The Attempt at a Solution

Given that the arm and hinge lengths are constant, I've calculated all the geometry to determine exactly where the weight is at any time relative to the origin (center of circle), and the radius of the weight to the center of rotation (which changes with every degree of rotation of the arm). If I know the angular velocity, how can I calculate the forces? I'm a math guy and and am very very rusty on physics...

I hope the picture helps describe the scenario...

Thanks for any insight you can provide I'm very grateful++

 

[DEvens]

Going to need to see you do at least something. The force that keeps the weight moving in the circle is given by the formula. But you have to work out what other forces are available.

What are they? Start by listing all of the forces in the problem. What assumptions will you make in order to get those forces? For example: Is this thing rotating on a table with the arm extending parallel to the surface of the table? Or is it rotating vertically? Mr. Subliminal describes the gravity of the situation.

 

[DrTuring]

Thanks @DEvens .

It's rotating in the vertical plane and I think safe to assume in a vacuum so gravity can be ignored.

I may be horribly mistaken, and please help correct me, but I think then the forces acting on the weight are from the hinge pulling on it towards the hinge's rotation point and the arm pulling on the hinge towards the arm's rotation point..

Does that sound right? So at any frame I calculate those angles (based on the circular path) and try to get a net acceleration vector?

 

[DrTuring]

Ah and actually then wouldn't the centripetal acceleration just be the line from the weight to the rotation point (because of vector addition)? Like the hypotenuse not drawn in the triangle above (rotation point, hinge point, weight point).

If I break that vector into x and y components can I just use F.x = m * a.x and F.y = m * a.y?

 

[DrTuring]

So I think I've got this, would anyone mind helping me check my work (@DEvens )? I might be totally going about this wrong

Assume the following values:

T = 0.1 sec
circleRadius = 50
circleOrigin = (0, 0)
armLength = 40
armPos = (10, 0) //the point the arm is rotating around
hingeLength = 30
weightMass = 1 // one because then I can omit it F=ma => F = a

for the frame where the arm is rotated 1 degree, I calc the weight's position to be (41.3, -28.0)

next I find the distance from the weight to the center of rotation (armPos)
weightDist = weightPos - armPos = (31.4, -28.0)

I calculate the magnitude of this position vector to get R
R = 42.1

Now I can calc acceleration ac = (4 * pi^2 * R) / T^2 = about 166000

using the weight's rotation around the origin (-34 deg), I can find x,y components of ac:
ac_x = 137589
ac_y = -93209

Does that sound right? I really have no idea if I'm totally wrong about this... If ac is towards the center does that mean that the weight pushes the circle in the opposite direction?

Please help!

 

[DrTuring]

Did I ask the question wrong? Sorry y'all I'm trying...