mechanics question

[Guest aether]

my first post here. quite a newbie. wondering if you people could help me out here. doesn't seem like a hard question (but i can't seem to do it). anyway here goes.

 

consider a bead on a wire that is rotating at constant angular velocity. the wire's horizontal and there's no friction between the surfaces. It would seem that the bead would swing out horizontaly on the wire (lookin at the bead system) and would form a spiral (looking at the whole system from the outside). Now, we can also work out that there is an acceleration goin outwards(horizontally). How can we account for this outward acceleration in forces? real forces i mean.

 

thanks

[Thales]

The outward acceleration force (sometimes reffered to as centripetal) is an illusion that comes about from newtons first law. (Ie an object would like to continue on a straight line unless a force acts upon it) In this case the tension in the string 'pulls' the bead off its preferred tangential motion resulting in a circular path.

 

Try to remember acceleration is a vector quatity and thus, a constant speed that changes direction is the result of an acceleration.

 

There is an abundance of forumlas for constant circular acceleration which will give you a numerical value for this force.

[Guest aether]

thanks for your post. think you're refering to centrifugal force. it's a force that's dependant on your frame of reference and is there when you consider the rotating frame. yea, and it is imaginary

 

anyway, think you misunderstood my question. the bead is able to traverse freely on the wire ( ie. no friction no extra strings and it's not tied to anything) . Also, just to clarify the question, we can see that the only forces acting on it are by the wire which implies that force acting on the bead is tangential to motion or it's velocity.

 

now what i'm tryin to find out is the radial force which pushes the bead out (seemingly to infinity) .

 

thanks

[Thales]

Centrifugal, correct. Its because the bead wants to stay still and the wire is applying a force to the bead due to friction, it begins to slide because the friction coefficient isn't equal to one, if it is(=1)the bead is stuck and it moves in a circle with the wire.

[swansont]

now what i'm tryin to find out is the radial force which pushes the bead out (seemingly to infinity) .

 

There is no radial force. It's an illusion because you are in a rotating reference frame when you look at it from the wire or bead's point of view. The force is always tangential in an inertial frame.