Angular velocity: dθ/dt = ω = 12t 2,

Angular acceleration: dω/dt=α=24t,

1, then the tangential acceleration is at = α r = 2.4t = 4.8m/s 2.

2. From the meaning of the question, we can get the equation: ω 2r = α r, (12t 2) 2r = 24tr.

144 t 4 = √ 3 (24t), which is sorted as: t 3 = √ 3/6,

From θ = 2+4t 3, we can get θ = 2+4 * √ 3/6 = 2+2 * 0.58 = 2+1.16 = 3.16 (rad).

From the tangential acceleration is equal to half of the total acceleration, it can be concluded that centripetal acceleration is equal to √3 times of the tangential acceleration.