MHT CET · Physics · Motion In Two Dimensions
If \(\alpha\) is angular acceleration, \(\omega\) is angular velocity and \(a\) is the centripetal acceleration then, which of the following is true?
- A \(\alpha=\frac{\omega a}{v}\)
- B \(\alpha=\frac{v}{\omega a}\)
- C \(\alpha=\frac{a v}{\omega}\)
- D \(\alpha=\frac{a}{\omega v}\)
Answer & Solution
Correct Answer
(A) \(\alpha=\frac{\omega a}{v}\)
Step-by-step Solution
Detailed explanation
Centripetal acceleration,
\(\because\) \(\alpha=\frac{\omega}{t}\)
\(\begin{aligned}\therefore \alpha &=\frac{\omega v}{v t} \\&=\frac{\omega a}{v}\end{aligned}\)
\(\because\) \(\alpha=\frac{\omega}{t}\)
\(\begin{aligned}\therefore \alpha &=\frac{\omega v}{v t} \\&=\frac{\omega a}{v}\end{aligned}\)
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