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 ? = 70

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 ? = 70 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/s^2.

Explanation / Answer

Applying energy conservation

Potential energy loss = rotational kinetic energy gain

MgL/2 sin(70) = 1/2*(ML2 /3) * w2

w = sqrt [ 3g/L* sin(70) ] = 5.26 rad/sec (ans)

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