A thin, uniform rod is hinged at its midpoint. To begin with, one half of the ro
ID: 2108187 • Letter: A
Question
A thin, uniform rod is hinged at its midpoint. To begin with, one half of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 8.4 rad/s about an axis that is perpendicular to the left end of the rod and parallel to the rod?s upward half (see the drawing). Without the aid of external torques, the rod suddenly assumes its straight shape. What is the angular velocity of the straight rod?
A thin, uniform rod is hinged at its midpoint. To begin with, one half of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 8.4 rad/s about an axis that is perpendicular to the left end of the rod and parallel to the rod?s upward half (see the drawing). Without the aid of external torques, the rod suddenly assumes its straight shape. What is the angular velocity of the straight rod?Explanation / Answer
L = Iw = Constant
Inital Moment of Inertia = (1/3)*(M/2)*(L/2)^2 + (1/3)*(M/2)*(L/2)^2 + (M/2)*(L/2)^2
= (5/6)M*(L/2)^2
= (5/24)ML^2
Final Moment of Inertia = (1/3)ML^2
Therefore
w*(1/3)ML^2 = 6.2 * (5/24)ML^2
w = 3.875 rad/sec
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