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 = 0.210 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?

Explanation / Answer

First we normalize the equation which is required The total moment of inertia of the loop is
        I = [(mL2 /12 + mL2 / 4] + 0.5mR2 + m(L+R)2            = mL2 / 3 + 0.5mR2 + m(L+R)2
Given that
           L =1.0 R
           R =0.210 m
Substitute values and solve for I.
Now according to conservation of energy we have
          0.5I2 = m g L + 2 m g (L+R)
    ==> = [ 2* (m g L + 2 m g(L+R)) /   I ] By substituting the values in the above equation we get the required value

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.