A stick is resting on a concrete step with 1/6 of its length hanging over the ed

Question

A stick is resting on a concrete step with 1/6 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 3.09 times the mass of the stick and the stick is 15.1 cm long, what is the magnitude of the angular acceleration of the stick at the instant shown?

Print Calculator Periodic Table Question 3 of 7 Map Sapling Learning macmillan learning A stick is resting on a concrete step with 1/6 of its length 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 comin momentarily to rest 51.7° from the horizontal. If the mass of each bug is 3.09 times the mass of the stick and the stick is 15.1 cm long, what is the hanging over the e dge. A single ladybug 51.700 n age instanf she angular acceleration of the stick at the instant shown Number figure not to scale rad/s Previous Give Up &View; Solution Check Answer NextExit Hint

Explanation / Answer

let m is the mass of the rod.

so mass of each bug = 3.09*m

L = 15.1 cm = 0.151 m

moment of inertia of the system about the axis of rotation,

I = 3.09*m*(L/6)^2 + 3.09*m*(L - L/6)^2 + m*L^2/12 + m*(L/2 - L/6)^2

= (4367/1800)*m*L^2

Torque acting ord,

T = 3.09*m*g*(5*L/6)*sin(90 - 51.7) + m*g*(L/2 - L/6)*sin(90-51.7) - 3.09*m*g*(L/6)*sin(90 - 51.7)

= 1.483*m*g*L

now use, T = I*alfa

==> alfa = T/I

= 1.483*m*g*L/((4367/1800)*m*L^2)

= 13347*g/(21835*L)

= 13347*9.8/(21835*0.151)

= 39.7 rad/s^2

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