find out angular displacement of a particalthe

Question

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

At t = 2 sec

∴ ω = 48 - 12 = 36 rad / sec

At t = 2 sec

 α = d ² φ /d t ² = 24 t - 6

α = 48 - 6 = 42 rad / sec ² .