Question
Define average and instantaneous angular acceleration. Give the unit and dimensional formula of angular acceleration.
Solution
Average acceleration is the ratio of change in angular velocity of a particle to the time taken to undergo the change in angular velocity.
Let a particle be revolving with varying angular velocity.
Let at any instant t, the angular velocity of particle be
and at time t+∆t, it is ω+∆ω.
Therefore average angular acceleration of particle is,
In vector form,
Instantaneous acceleration is the acceleration of the particle at a particular instant and is equal to limiting value of the average acceleration of particle as the time interval approaches zero.
Mathematically,
Also,
Let a particle be revolving with varying angular velocity.
Let at any instant t, the angular velocity of particle be
and at time t+∆t, it is ω+∆ω. Therefore average angular acceleration of particle is,
In vector form,
Instantaneous acceleration is the acceleration of the particle at a particular instant and is equal to limiting value of the average acceleration of particle as the time interval approaches zero.
Mathematically,
Also,
