Angular Velocity/Motion Question

[Victorzaroni]

Homework Statement

A bead of mass m is free to slide along a frictionless ring of radius R=.5 meters that rotates about the vertical axis with angular velocity ω=6 rad/sec as shown below. What angle θ with the vertical will the bead make?

The answer choices are:
(A) 90
(B) 61
(C) 56
(D) 34
(E) 29

This is from the Physics C Mechanics: Sample Exam III.

Homework Equations

I have no idea.

The Attempt at a Solution

I don't know where to start.

 

[kushan]

Try to make Free body diagram , with all the forces

 

[Victorzaroni]

Okay, I did. I have an Fc pointing in, and an mg pointing down, but I'm still not seeing it.

 

[kushan]

see there will mg (weight )going downward and a normal reaction ,
then you take components of Normal reaction and solve :D

 

[kushan]

Here is the figure

 

[Victorzaroni]

ohh. okay. so we can use wr=v, and when Fn is mg, that way when we set up, the masses cancel, and we can solve for v. Thanks!

 

[kushan]

but remember in v=rw r is the radius of the motion of particle not the ring :O

 

[Victorzaroni]

oh. that's the d in your diagram. So the two radii are different. So how do I get this d?

 

[kushan]

simple trigo rsin(theta)= d

 

[Victorzaroni]

but we don't have ø?

 

[Victorzaroni]

I tried working it out multiple times, but no matter how I do it, with your d or without it, the fraction at the end never falls in the domain for the sin^-1. Can you write out what you would do? Thanks for all your help so far, in my other posts too.

 

[Victorzaroni]

Oh wait a minute, I think I got it. Perhaps d=rcosø? If so, then at the end, tan^-1((w²r)/g)=ø=61, choice B.

 

[kushan]

Yea , good going :)