HELP a question on angular velocity

[Kudo Shinichi]

HELP!a question on angular velocity

Homework Statement

A horizontal cylindrical rod is free to rotate about a vertical axis perpendicular to its length through its centre of mass. two beads of mass m and 2m are each a distance l from the axis of rotation and are tied together by a light string. the coefficient of static friction between each of the beads and the rod is mu(s). the rod accelerates from rest with a constant angular acceleration alpha. find the angular velocity of the rod at the instant the beads start to move along the rod, if mu(s)=1/12, l=2.0m (radius), and alpha=1.5rad/s

Homework Equations

centripetal or radial acceleration:
LaTeX Code: <BR>a_c = \\frac{v^2}{r} = r\\omega^2<BR>

tangential acceleration:
LaTeX Code: <BR>a_{\\rm tan} = r\\alpha<BR>

The Attempt at a Solution

first of all, I tried to find tangential acceleration:
a=radius*alpha
=2.0*1.5
=3m/s^2
than I have to solve for the centripetal acceleration:
a=v^2/r=r*omega^2
two unknown variables, so we have to solve for a
Frictional force=mu(s)*m*g
mu(s)=1/12 g=9.8
and
frictional force=ma
mu(s)*m*g=ma
a=1/12*9.8=0.8167
then omega=0.639
I am wondering, for this question which is the answer we want, omega or tangential acceleration? or others?

 

[JoAuSc]

You should not equate the tangential and centripetal acceleration. What you want to do is find the total acceleration on the beads. This is the tangential plus the centripetal accelerations. When we know what the total acceleration is, we can equate it with the force of friction and so forth.

 

[Kudo Shinichi]

You should not equate the tangential and centripetal acceleration. What you want to do is find the total acceleration on the beads. This is the tangential plus the centripetal accelerations. When we know what the total acceleration is, we can equate it with the force of friction and so forth.

total acceleration=sqrt(tangential acceleration^2+centripetal acceleration^2)
after we find the total acceleration, is it the answer we are looking for? if not can you tell me how to relate velocity to acceleration? thank you very much.

 

[JoAuSc]

The total acceleration is not the answer, the problem asks you to find the angular velocity, but you need to find the total acceleration to get there. Now, the total acceleration is a vector with one component being the tangential acceleration and the other component being the centripetal acceleration. You have calculated the magnitude of the total acceleration. (You probably know this, but I just want to be unambiguous.) Now, Newton's 2nd law states that

m*a_total = sum of forces

The total acceleration (vector) is pointing opposite the force of friction, so their magnitudes must be opposite. Thus,

m*|a_total| = mu*m*g

where |a_total| is the magnitude of the total acceleration. You know everything on the right side of this equation. You know almost everything on the left side except for the angular momentum, which you need to find the centripetal acceleration, which is part of |a_total|. You have an equation with one unknown, omega. Solve for omega.