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How we obtain this equation from Newton's second law

How we obtain this equation from Newton's second law-example-1
User Ben McNiel
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Just recall Newton's law of motion:

Recall S = (v + u)*t / 2. .................(1)
Similarly S will be replaced with θ,
v will be replaced with ω
u will be replaced with ω0

Therefore θ = (ω + ω0)*t / 2. .............. (2)

Recall from linear motion v = u + at.
For angular motion it would be ω = ω0 + αt ..............(3)

The linear acceleration a, is replaced with angular acceleration α

Substituting (3) into (2).

θ = ( ω + ω0) * t/2
θ = (ω0 + αt + ω0) *t / 2
θ = (2ω0 + αt) * t/2
θ = (2ω0t + αt^2) /2

θ = (ω0t + 1/2 * αt^2). (Q.E.D)

User Steve Sheldon
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