A stick is resting on a concrete step with 1/5 of its length hanging over the ed

Question

A stick is resting on a concrete step with 1/5 of its length hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest 56.9° from the horizontal. If the mass of each bug is 3.60 times the mass of the stick and the stick is 16.3 cm long, what is the magnitude of the angular acceleration of the stick at the instant shown? In radians per second.

Explanation / Answer

Here's the method.

Call the mass of the stick M.

Draw a diagram with the distances and angles clearly marked.

Using the standard formula, find the moment of inertia of the stick about its centre.

Using the parallel axis theorem, find the moment of inertia, I, of the stick about the pivot point.

Find the torque (moment) produced by the lower bug. This is
3.60Mg *(1/5)*(0.163)cos(56.9

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