The thin uniform rod in the figure has length 1.0 m and can pivot about a horizo

Question

The thin uniform rod in the figure has length 1.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle ? = 40

The thin uniform rod in the figure has length 1.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle ? = 40 A degree above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position. Assume free-fall acceleration to be equal to 9.83 m/s2.

Explanation / Answer

Energy conservation

Change in potential energy = rotational KE assuming pure rotation from end point

mgl/2 cos(40) = 1/2 ml^2/3 * w2

w = sqrt (3g cos(40) /L) = 4.752 rad/sec (ans)

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