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The ratio of the moment of inertia of the two objects A and B is 1 : 2. If the ratio of the angular velocity of the object A to object B is 2 : 1, then find the ratio of the angular momentum of the object A to object B.

  1. 1 : 1
  2. 1 : 4
  3. 4 : 1
  4. None of these

Answer (Detailed Solution Below)

Option 1 : 1 : 1
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Detailed Solution

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CONCEPT:

Angular momentum:

  • Angular momentum is the property of any rotating object given by moment of inertia times angular velocity.
    • It is a vector quantity.
    • Its SI unit is kg-m2/sec.
  • If I and ω are the moment of inertia and the angular velocity respectively, then the angular momentum is given as,

⇒ L = Iω

⇒ L = rP

Where r = radius of rotation and P = linear momentum

CALCULATION:

Given , and 

  • Angular momentum is the property of any rotating object given by moment of inertia times angular velocity.
  • If I and ω are the moment of inertia and the angular velocity respectively, then the angular momentum is given as,

⇒ L = Iω     -----(1)

  • By equation 1 the angular momentum of the object A is given as,

⇒ LA = IAωA     -----(2)

  • By equation 1 the angular momentum of the object B is given as,

⇒ LB = IBωB     -----(3)

By equation 2 and equation 3,

  • Hence, option 1 is correct.

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