A stick is resting on a concrete step with 2/11 of its length hanging over the e

Question

A stick is resting on a concrete step with 2/11 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 51.7° from the horizontal. If the mass of each bug is 2.75 times the mass of the stick and the stick is 17.5 cm long, what is the magnitude of the angular acceleration of the stick at the instant shown?

Explanation / Answer

on hanging edge

m1 = 2.75 M

x1 = 2L/11

opposite edge

m2 = 2.75 M

x2 = 9L/11

net torque = M*g*L/2*cos51.7 + m2*g*x2*cos51.7 - m1*x1*cos51.7

net torque = M*g*L/2*cos51.7 + m2*g*9L/11*cos51.7 - m1*2L/11*cos51.7

net torque = [ (0.5) + (2.75*(9/11))   - (2.75*(2/11)) ]* M*g*L

net torque = 2.25*M*L*g

torque = I*alfa

I = (1/12)M*L^2 + M*(L/2-2L/11)^2 + m1*x1^2 + m2*x2^2

I = ( (1/12) + 0.32 + (2.75*(2/11)^2) + (2.75*(9/11)^2) )M*L^2

I = 2.34*M*L^2

2.25*M*L*g = 2.34*M*L^2*alfa

2.25*9.8 = 2.34*0.175*alpha

alpha = 53.8 rad/s^2 <<-----answer

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