Rotating Buckets

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.

Two buckets connected by a rod rotating anti-clockwise.

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

Answer Section#

Part 2#

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 \(\omega_f = \omega/\)3. How much rain (in kg) has been collected by the two buckets? When empty, the buckets each have a mass of 2.25 kg.

Answer Section#

Please enter in a numeric value in kg.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.