- #1
Kudo Shinichi
- 109
- 1
HELP!a question on angular velocity
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
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>
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 accleration? or others?
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 accleration? or others?