A thin rod (length = 1.94 m) is oriented vertically, with its bottom end attache

Question

A thin rod (length = 1.94 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. (a) What is the angular speed of the rod just before it strikes the floor? (Hint: Consider using the principle of conservation of mechanical energy.)(b) What is the magnitude of the angular acceleration of the rod just before it strikes the floor?

Explanation / Answer

here the initial energy of the massless rod with the mass at tip has =mgh where m is mass attached and g is accel due to gravity and h is length if rod here let h=L...
and final energy will be =1/2 x Ix ^2           where I= moment of inertia of the mass =mL^2

and =angular velocity....................

know

initial energy=final energy ............ as energy is conserved

         mgL=(1/2 ) I ()^2

        =( 2mgL/I)^(1/2)

        =( 2mgL/m(L)^2)^(1/2)

        =(2g/L)^(1/2)

hence we obtained the w

for alfa=a=/t

       hence a=((2g/L)^(1/2))/t            where we get t from the equation of kinematics.....

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