(a) Show by integration that the moment of incrtia ofa thin uniform rod, of mass m and length 20 ubout an axis through one end and perpendicular to the rod, is ma 3
(a) Show by integration that the moment of incrtia ofa thin uniform rod, of mass m and length 20 ubout an axis through one end and perpendicular to the rod, is ma 3
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Answer 7a
Transcribed Image Text:7.
Show by integration that the monment of incrtia of a thin uniform rod, of mass m and length
(a)
20 about an axis through one end and perpendicular to the rod, is
-ma
3
A thin unilorm rod AB ol mass 3ni and length 2a attached to a fixcd hinge at the end A, hangs freely
in cyuilibrium. The end B is given a small horizontal push so that the rod oscillates through a small
angle in a vertical plane.
Show that the eqquation of motion of the rod can bc expressed in the form
(b)
(i1)
d0
= 3g cos0 - K
dr
where 0 is the angle thai AB makes with the downwanl vertical through A and K is a constant.
Find
(ii) the radius of gyration of the rod ahout the axis through the hinge.
(iii) the period of small oscillations of the rod.
(iv) the length of the equivalent simple pendulum,
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