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Laws Of Motion

Question
CBSEENPH11016891

Derive the relation ω = ω0 + at for uniform angular accelerated motion.

Solution
Let a particle revolve in a circular orbit with constant angular velocity straight omega.
Let the particle start from ω0 and start accelerating with angular acceleration straight alpha.
Let straight omega be the angular velocity at any instant.
We know,
space space space space space space space straight alpha space equals space dω over dt
rightwards double arrow space dω space equals space space straight alpha space dt space

Integrating space both space sides comma space

space space space space space space space space integral subscript straight omega subscript straight o end subscript superscript straight omega d straight omega space space equals space integral subscript 0 superscript straight t straight alpha d straight t space equals space straight alpha integral subscript 0 superscript straight t dt space

rightwards double arrow space space space right enclose straight omega subscript straight omega subscript straight o end subscript superscript straight omega space equals space right enclose αt subscript 0 superscript straight t space

rightwards double arrow space space space straight omega space minus space straight omega subscript straight o space equals space αt

rightwards double arrow space space space straight omega space equals space space straight omega subscript straight o space plus space αt space 
Hence, the result.