Angular Acceleration

When we start a motor, the angular velocity of the shaft starts at ω = 0 and increases until the motor gets up to its normal speed.

..........(i)

During this start-up, ω t changes with time, and we have an angular acceleration α defined by
............ (1)
The angular acceleration α has the dimensions of rad ians/sec² since the derivative gives us another factor of time in the denominator. Combining Equation (i) and (1) relates α to θ by

...........(2)