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If a body is rotating with variable angular acceleration, which of the following equation can be used to get angular velocity?
1. ω1 = ω0 + α t
2. ω12 = ω02 + 2 α θ
3. Both 1 and 2 can be used
4. Neither 1 nor 2 can be used

1 Answer

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Correct Answer - Option 4 : Neither 1 nor 2 can be used

CONCEPT:

  • Angular velocity (ω): How fast the angular position or orientation of an object changes with time or How fast an object rotates or revolves relative to another point is known as angular velocity.
  • Angular acceleration (α): The rate of change of angular velocity is known as angular acceleration.


The relation between α and changing ω is given by: 

  • Three equations to be used when α is constant:
  1. ω1 = ω0 + α t
  2. θ = ω0t + 1/2 α t2
  3. ω12 = ω02 + 2 α θ


​where ω1 is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration and θ is angular displacement.

EXPLANATION:

  • Three equations that shows the relation between α and changing ω to be used when α is constant:
  1. ω1 = ω0 + α t
  2. θ = ω0t + 1/2 α t2
  3. ω12 = ω02 + 2 α θ
  • ​Since in the question, it is given that angular acceleration α is variable
    • so we cannot use any of the above equations.
  • For variable angular acceleration, we have to solve it by integration.

\(\omega =\int \alpha .dt\)

  • Hence the correct answer is option 4.

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