10/12/2017 11:00 PM 76.8/100 O 10/10/2017 04:52 PM Gradebook Question 12 of 14 S

Question

10/12/2017 11:00 PM 76.8/100 O 10/10/2017 04:52 PM Gradebook Question 12 of 14 Sapling Learning Map 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 comin 62.100 mass of each bug is 2.75 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? figure not to scale rad/s

Explanation / Answer

Torque taking the point B as the axis of rotation is given as

Torque = m1g Cos62.1 (AB) - m2g Cos62.1 (BC) - Mg Cos62.1 (BD)

Torque = (2.75) MgCos62.1 (L/5) - (2.75) MgCos62.1 (4L/5) -  Mg Cos62.1 (L/2 - L/5)

Torque = (MgCos62.1) (L) ((2.75/5 ) - (2.75) (4/5) - (0.3))

Torque = (0.912) Mg

moment of inertia of the system is given as

I = m1 (AB)2 + m2 (BC)2 + (1/12) M L2

I = (2.75 M) (L/5)2 + (2.75 M) (4L/5)2 + (1/12) M L2

I = (0.11 + 0.44 + 0.5) (M L2 )

I = (1.05) M L2 = (1.05) M (0.163)2 = 0.028 M

angular acceleration is given as

a = Torque /I =  (0.912) Mg /(0.0298 M) = 299.92

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