When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)?

By using equation ω2=ω02−2αθω022=ω02−2α(2πn)⇒α=34ω024π×36,(n=36)   .......(i)Now let fan completes total n' revolution from the starting to come to rest0=ω02−2α2πn′⇒n′=ω024απSubstituting the value of α from equation (i)n′=ω024π4×4π×363ω02=48 revolutions Number of rotation = 48 - 36 = 12