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A thin uniform rod of mass M and length L is hinged vertically above frictionless pivot point O, as shown in figure and then allowed to fall to the ground. With what angular speed does rod strike the ground?

A thin uniform rod of mass M and length L is hinged vertically above frictionless pivot point O, as shown in figure and then allowed to fall to the ground. With what angular speed does rod strike the ground?

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Grade:12

3 Answers

Saurabh Kumar
askIITians Faculty 2400 Points
9 years ago
Consider a momentary situation at an angle with the horizontal..
calculate the torque or angular momentum about the centre of mass that will be equal to the (I a or I.w)
where, I is moment of inertia, a is angular acceleration, w is angular velocity.....
Saurabh Kumar
askIITians Faculty 2400 Points
9 years ago
write the equartion for angular momentum conservation at any instant making angle with vertical, i.e. mvl= Iw
2. Loss in potential energy = gain in Rotational kinetic energy
mgl/2/1(1-cos@) = 1/2Iw2
solve, in this way and calculate...
sajid
615 Points
8 years ago
write equation of ang.momentum conservation with angle vertical =>mvl=lw
loss of potential energy = gain in rotational kinetic energy =>mgl/2/1(1-cos@)=1/2lw2
and calculate

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