vector. Further, the angular acceleration, α = d ω /d t . The kinematical quantities in rotational motion, angular displacement ( θ ), angular velocity ( ω ) and angular acceleration ( α ) respectively are analogous to kinematic quantities in linear motion, displacement ( x ), velocity ( v ) and acceleration ( a ). We know the kinematical equations of linear motion with uniform (i.e.
constant) acceleration: v = v + at (a) at υ (b) ax υ υ (c) where x = initial displacement and v = initial velocity. The word ‘initial’ refers to values of the quantities at t = The corresponding kinematic equations for rotational motion with uniform angular acceleration are: ( . ) ( . ) and ( – α θ ( .
) where θ = initial angular displacement of the rotating body, and ω = initial angular velocity of the body. Fig. . Specifying the angular position of a rigid body.
Example . Obtain Eq. ( . ) from first principles.
Answer The angular acceleration is uniform, hence constant (i) Integrating this equation,