Question

Two bodies have their moments of inertia
1 and 21 espectively about their axis
rotation are equal then what is
ratio of their angular velocity
​

Answer 1

Consider two bodies A and B are having moment of inertia Iand2I

KA= Kinetic energy of rotation for the body A=(1/2)Iω2A where, ωA is angular speed of the body A

KB= Kinetic energy of rotation for the body B=12(2I)ω2B

According to the question, KA=KB

⇒12Iω2A=12(2I)ω2B⇒ω2A=2ω2B⇒(ωAωB)2=2

⇒ωAωB=2–√⇒ωA:ωB=2–√:1.