Find out angular displacement of a partical:
The angular displacement of a rotating body starting from rest is defined by φ (t ) = 4 t ^{3} - 3 t ^{2} . Find out its angular displacement, angular velocity and angular acceleration at t = 2 sec.
Solution
At t = 2 sec
φ = 32 - 12 = 20 radians
ω= d φ/dt = 12 t ^{2 }- 6 t dt
∴ ω = 48 - 12 = 36 rad / sec
α = d ^{2} φ /d t^{ 2} = 24 t - 6
α = 48 - 6 = 42 rad / sec ^{2} .