A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle phi as omega = omega_0 - k phiwhere omega_(0)and k are positive constants. At the moment t = 0, phi = 0, the time dependence of rotation angle is

A solid body rotates about a stationary axis so that its angular veloc

1.	A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle phi as omega = omega_0 - k phiwhere omega_(0)and k are positive constants. At the moment t = 0, phi = 0, the time dependence of rotation angle is
Answer» `K omega_(0) e^(-kt)` `(omega_(0))/(k) e^(-kt)` `(omega_(0))/(K) (1 - e^(-kt))` `(k)/(omega_(0)) (e^(-kt) - 1)` SOLUTION :As `omega = omega_(0) - k phi` (GIVEN ) `therefore (d phi)/(DT) = omega_(0) - k phi` or `int_(0)^(phi) = (d phi)/(omega_(0) - k phi) = int_(0)^(t) dt` or `- (1)/(k) [ ln (omega_(0) - k phi)]_(0)^(phi) = t ` or ln `((omega_(0) - k phi)/(omega_(0))) = - kt ` `therefore phi = (omega_(0))/(k) ( I - e^(-kt))`