# Rotating Buckets#

A pair of buckets are connected by a massless rod. As shown in the figure, the buckets rotate about an axis through the centre of mass of the two-bucket system.

## Part 1#

If each bucket has a mass $$m$$ and the rod has length $$l$$, what is the rotational inertia of the system? Give your answer in terms of $$m$$ and $$l$$. Treat the buckets as point masses and recall that $$I = \sum\limits_i m_ir_i^2$$.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

$$m$$

m

$$l$$

l

Assume that initially the buckets rotate with angular speed $$\omega_0$$. Then it rains for a short time. After the rain has stopped, the buckets are observed to be rotating with angular speed $$\omega_f = \omega/$$5. How much rain (in kg) has been collected by the two buckets? When empty, the buckets each have a mass of 1.65 kg.