A thin rod A B is held horizontally so that it can freely rotate in a vertical plane about the end A as shown in the figure. The potential energy of the rod when it hangs vertically is taken to be zer

Question

A thin rod A B is held horizontally so that it can freely rotate in a vertical plane about the end A as shown in the figure. The potential energy of the rod when it hangs vertically is taken to be zero. The end B of the rod is released from rest from a horizontal position. At the instant the rod makes an angle θ with the horizontal

TestHub · Accepted Answer

Loss in potential energy = gain in kinetic energy ⇒ m g 2 L ​ sin θ = 2 1 ​ I ω 2 So ω ∝ sin θ ​ and v ∝ sin θ ​ ( ∵ K = 2 1 ​ H ω 2 ) The speed of end B is proportional to sin θ ​ and U = m g h = m g 2 L ​ ( 1 − sin θ ) ( ∵ τ = l α ) ⇒ m g 2 L ​ cos θ = 3 m I 2 ​ × α α ∝ cos θ The angular acceleration is proportional to cos θ

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