The angular velocity of the rigid body is given by
ω=α−βt, where
α and
β are constants. By comparing this with the equation
ω=ω0−αt, we can identify the initial angular velocity
ω0 as
α and the angular retardation (or deceleration) as
β.
To find the angle through which the body rotates before it comes to a stop, we use the kinematic equation for rotational motion:
ω2=ω02+2βθWe know that when the body stops,
ω=0. Therefore, by substituting into the equation, we get:
0=α2−2βθSolving for
θ, the angle rotated, we find:
θ=‌Thus, the angle through which the body rotates before stopping is
‌.