A disc is rotating at an angular velocity omega_(0). A constant retardation torque is applied on it to stop the disc. After a certain time at which some number of rotation of the disc have been performed so that total angle rotated is theta_(1) and that only 2/3 th of these ratios will further stop the disc. find the retarding force.

A disc is rotating at an angular velocity omega_(0). A constant retard

1.	A disc is rotating at an angular velocity omega_(0). A constant retardation torque is applied on it to stop the disc. After a certain time at which some number of rotation of the disc have been performed so that total angle rotated is theta_(1) and that only 2/3 th of these ratios will further stop the disc. find the retarding force.
Answer» `(11 omega_(0)^(2))/(14 theta_(1))` `(9omega_(0)^(1))/(14 theta_(1))` `(5 omega_(0)^(2))/(14 theta_(1))` `(3 omega_(0)^(2))/(14 theta_(1))` Solution :Let `n_(1)` rotations performed UPTO a certain time `n_(1)=(theta_(1)//2pi)` `n_(2)=2/3n_(1)=2/3((theta_(1))/(2pi))=(2/5 theta_(1)).1/(2pi)` `omega_(0)^(2)=omega_(0)^(2)-2alphatheta_(1).....(1)` and `0=omega_(1)^(2)-2alpha(2/5 theta_(1)).....(2)` From eqns. `(1)` and `(2)` `(4alphatheta_(1))/5=omega_(0)^(2)-2alphatheta_(1), alpha=(5 omega_(0)^(2))/(14 theta_(1))`