How to find angular acceleration....

The angular displacement of a particle is given by

𝜃= 〖6𝑡〗^2−4𝑡+6, where time ‘t’ is in second and 𝜃 is in rad. The angular acceleration of particle at t = 4 sec

a) 6 𝑟𝑎𝑑 𝑠^(−2)                       b) 24 𝑟𝑎𝑑 𝑠^(−2) 

c) 12 𝑟𝑎𝑑 𝑠^(−2)                     d) 48 𝑟𝑎𝑑 𝑠^(−2)

solution:

𝜃= 〖6𝑡〗^2−4𝑡+6

w. k .t. Angular velocity is time  rate of change of angular displacement.

𝜔=𝑑𝜃/𝑑𝑡=  𝑑/𝑑𝑡  (〖6𝑡〗^2−4𝑡+6)

𝜔= 12𝑡−4+0

Also,

An acceleration is time rate of change of angular velocity

𝛼=𝑑𝜔/𝑑𝑡=𝑑/𝑑𝑡(12𝑡−4)

𝛼=12 𝑟𝑎𝑑𝑠^(−2)