A slender bar of mass m = 1 kg and length l = 1 m is acted upon by a torsion spr

Question

A slender bar of mass m = 1 kg and length l = 1 m is acted upon by a torsion spring at O which exerts a counter-clockwise couple M = 10 Nm on the bar as it swings past the vertical position. If the angular velocity of the bar is 10 rad/s at the vertical position as shown, find the n- and t-components of the bearing reaction on the bar at that instant. You can assume that g - 10 m/s2. For the slender bar, the moment of inertia about O is I_O = 1/3ml^2 and that about the center of gravity is I_cG = 1/12 ml^2,

Explanation / Answer

As, Torque = Moment of inertia * angular acceleration

=> Force * Radius =   Moment of inertia * angular acceleration

=> n - component of bearing reaction = [1/3 * 1 * 12 * (10/1)]/(1)

                                                       = 3.33    N

=> t - component of bearing reaction = 10/ [1/12 * 1 * 12 ] * 1 * 1

                                                          = 120    N

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