2) [8 pts] A uniform rod of mass M and length L is standing vertically on its en

Question

2) [8 pts] A uniform rod of mass M and length L is standing vertically on its end, which is fixed in position to the floor but able to pivot. The rod is initially at rest, but then is nudged very gently and pivots around its end as it falls to the floor. (The moment of inertia of a uniform rod of mass M and length L, rotating around its end, is 1/3 ML-) a. Calculate the rod's angular speed an instant before it hits the floor b. Calculate its angular acceleration an instant before it hits the floor. pivot Phys 131 Final, Dec 10th, 2013 Page 4 34

Explanation / Answer

2. (a) Applying energy conservation,

PEi + KEi = PEf + KEf

M g (L/2) + 0 = 0 + I w^2 /2

{ I = M L^2 / 3 }

M g L / 2 = ( M L^2 / 3) w^2 / 2

w = sqrt[ 3g / L ]

(B) for angular acc.,

torque = I alpha

(M g L /2 sin90) = (m L^2 / 3) alpha

alpha = 3 g / 2 L  

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