A stick is resting on a concrete step with 1/3 of its length hanging over the ed

Question

A stick is resting on a concrete step with 1/3 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 41.3 degree from the horizontal. If the mass of each bug is 2.75 times the mass of the stick and the stick is 11.5 cm long, what is the magnitude of the angular acceleration of the stick at the instant shown?

Explanation / Answer

First we calculate moment of inertia about CM = ml2/12

Now calculating the moment of inertia of the stick about which it is rotating

Using parallel axis theorem

I' = ml2/12+m(l/6)2

or, I'= 14.69m kgcm2

Now Writing the torque equation about the point of rotation

- 2.75m*(l/3)cos(41.3) + 2.75m*(2l/3)cos(41.3) + m*(l/6)*cos(41.3) = I'*alpha

9.270*m = 14.69*m*alpha

alpha = 0.6310 rad/s2 clockwise

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