## Pivoted Rod with Unequal Masses

The figure shows a simple model of a seesaw. These consist of a plank/rod of mass m_{r} and length 2x allowed to pivot freely about its center (or central axis), as shown in the diagram. A small sphere of mass m_{1} is attached to the left end of the rod, and a small sphere of mass m_{2} is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward. The magnitude of the acceleration due to gravity is equal to g.

**A) What is the moment of inertia ***I** *of this assembly about the axis through which it is pivoted?

**B) Suppose that 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 answered the first part correctly.)**

What is the angular acceleration α of the rod immediately after it is released?

A small sphere of mass m_{1} is attached to the left end of the rod, and a small sphere of mass m_{2} is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward. The magnitude of the acceleration due to gravity is equal to g.

**A) What is the moment of inertia ***I** *of this assembly about the axis through which it is pivoted?

**B) Suppose that 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 answered the first part correctly.)**

What is the angular acceleration α of the rod immediately after it is released?

## Answer ( 1 )

A) x^2(m_1+m_2+1/3m_r)

B) α= ((m_1-m_2)gx) / I