Question

If angular velocity of a disc depends an angle rotated as = 2 + 2, then its angular acceleration at = 1 rad is

Answer 1

Given:

w = Ф² + 2* (Ф)

As we know that,

angular acceleration= α

α= dw/ dt

α= dw/ dФ * dФ/ dt

therefore,

dФ/ dt = w

α= dw/ dФ * w

or,

α = w * dw/ dФ

α = w * d/dФ (Ф² + 2Ф)

α = (Ф² + 2Ф)  (2Ф + 2)

α = 2Ф² + 2Ф + 4Ф² + 4Ф

α = 6Ф² + 6Ф

α = 6Ф * (Ф + 1)

α= 6 * 1 * (1+ 1)

where, Ф =1

α = 12 rad/ sec²