A thin rod of mass mr and length 2L is allowed to privot freely its center as sh

Question

A thin rod of mass mr and length 2L is allowed to privot freely its center as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. What is the moment of inertia I of this assembly about the axis through which it is pivoted? Express the moment of inertia in terms of mr, m1, m2, and L. Remember, the length of the rod is 2L, not L. Suppose the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answer the first part correctly.) What is the angular acceleration alpha alpha of the rod immediately after it is released? Take the counterclockwise direction to be positive. Express alpha in terms of some or all of the variables mr, m1, m2, L, I, and g.

Explanation / Answer

a) MOI of rod about pivot = m_r*(2l)^2/12 = m_r*(l^2)/3

MOI of total assembly = MOI of rod + masses

= m_r*(l^2)/3 + m1*l^2 + m2*l^2

= (l^2)*(m_r/3 + m1 + m2)

b) Torque = I

(m2*g)*L - (m1*g)*L = I

= (m2 - m1)*gL/I

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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