Object sliding up/down with a angular speed

[MechaMZ]

Homework Statement

This is a concept question rather than a homework question, so i don't have any value for the question.

From the figures below, the object is turning horizontally. how do we know the object will start sliding up or sliding down at what angular velocity if there is no angular acceleration. Let's assume there is a friction force along the sliding path.

http://img199.imageshack.us/img199/8453/p667.gif http://img21.imageshack.us/img21/520/slideupordown.jpg

The Attempt at a Solution

1. What kind of friction coefficient should we use, static friction or kinetic friction?
2. I've draw out the free body, but still can't figure out the way to know the object will start to move at what angular speed? but i believe the free body diagram of both situations are the same.

http://img29.imageshack.us/img29/4503/slidedown.jpg

by using sum of F_{along the sliding path} = m(a_ccos [tex]\vartheta[/tex])?

 

[Redbelly98]

Since the object is initially not sliding, use the static friction coefficient to figure out when it will start sliding.

I think you're correct, using

sum of Falong the sliding path = m ( a_c cos θ )?​

should work. But I haven't worked this out myself.

 

[MechaMZ]

should i assume sum of F_{along the sliding path} = 0 if the angular speed is just nice without any sliding?

 

[MechaMZ]

I'm referring to the motion below:
http://img199.imageshack.us/img199/8453/p667.gif

and i have draw out the free body diagram when the object is about to sliding down.
http://img30.imageshack.us/img30/4503/slidedown.jpg

i'm confuse where should the Nsin[tex]\vartheta[/tex] place at? or do i need to resolve the N to Ntan[tex]\vartheta[/tex] and in the direction opposite the mgsin[tex]\vartheta[/tex] instead?(diagram below)

http://img35.imageshack.us/img35/4503/slidedown.jpg

for the centripetal acceleration,
sum of F_c=ma_c
N-mgcos[tex]\vartheta[/tex]=ma_c

for the sliding path,
sum of F_{sliding path}=ma_ctan[tex]\vartheta[/tex]
mg sin[tex]\vartheta[/tex] - friction force = ma_ctan[tex]\vartheta[/tex]

if my assumption is correct, then where should i put the Nsin[tex]\vartheta[/tex]? or change it to Ntan[tex]\vartheta[/tex] and place it along the sliding path??

 

[rl.bhat]

ac is the centripetal acceleration of the object on the vertical motion along the circle. The object is also describing horizontal circular motion. What is the centripetal acceleration for this motion? Position of the object on the vertical circle will be decided by this acceleration.

 

[MechaMZ]

ac is the centripetal acceleration of the object on the vertical motion along the circle. The object is also describing horizontal circular motion. What is the centripetal acceleration for this motion? Position of the object on the vertical circle will be decided by this acceleration.

could you explain in more detail? because i really don't understand =(

 

[rl.bhat]

When the object is turning horizontally,it will be pushed away from the axis of rotation, just like a passenger is pushed outward in a turning car. This force is equal to m(ω^2)r. One component of this force pushes the object up on the circular loop, and the other component contributes to the normal reaction. Its upward push is opposed by the component of the weight and frictional force. Other component of weight contributes to the normal reaction.