The figure below shows a rigid assembly of a thin hoop (of mass m and radius R =

Question

The figure below shows a rigid assembly of a thin hoop (of mass m and radius R = 0.130 m) and a thin radial rod (of mass m and length L = 1.00 R). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in such a nudge is negligible, what would be the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

rad/s: ????

Explanation / Answer

moment of inertia of the combined system along hte axis

= (ml^2/3 ) + mr^2/2 + m(r+l)^2

l=2.5R

= mr^2(6.25/3 + 1/2 + 12.25)

=mr^2(2.08+.5+12.25)

=14.83mr^2

no

distance of centre of mass from the axis

= (m(l/2) + m(r+l))/2m

=l/4 + r/2 + l/2

=(3l+r)/4

=2.125r

so

word done = change in K.E

2m*g*2*2.125r = .5*14.83mr^2*w^2

2*83.3mr= 14.83mr^2w^2

11.23/r =w^2

w^2=11.23/.130

w=9.29 rad/sec

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