Correct Answer - Option 4 : Neither 1 nor 2 can be used
CONCEPT:
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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.
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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:
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Three equations to be used when α is constant:
- ω1 = ω0 + α t
- θ = ω0t + 1/2 α t2
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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:
- ω1 = ω0 + α t
- θ = ω0t + 1/2 α t2
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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.