A long uniform rod of length L and mass M is pivoted about a frictionless, horiz

Question

A long uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is nudged from rest in a vertical position as shown in the figure below.

=(3g/L)

=1.5g/L

(c) At the instant the rod is horizontal, find the x and y components of the acceleration of its center of mass. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

ax=

ay=

(d) At the instant the rod is horizontal, find the components of the reaction force at the pivot. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

Rx=

Ry=

Explanation / Answer

Acceleration is ax = -r ?^2 = - (L/2) (3g/L) = -3g /2 ay = - r a = - (L/2) ( 3)g/2L = -3g/4 Newton second law Rx = M ax = M(3g/2) = - 3Mg/2 Ry - Mg = M ay Ry = Mg + May = Mg + M (-3g/4) = Mg /4

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