Like impulse in translational motion, we define angular impulse in rotational motion. When an external torque is acting on a rotating body, the rate of change of angular momentum gives the magnitude of the torque acting. Using the logic, the product of torque and time for which the torque is acting on the body, gives the total change in angular momentum of the body which is called angular impulse applied on the body.
To understand the concept of angular impulse, see the video – https://youtu.be/HTxWViEW4EI
For the case if applied torque is constant, the impulse can be calculated by product of torque and the time and in case of applied torque is varying with time, we integrate the product of torque with elemental time dt during the course of motion for the time of motion.
Kinetic Energy in Rotational Motion: As a fundamental term kinetic energy is defined as half of the product of mass and square of the speed of the body in case a body is in translational motion. Rotational motion is defined for extended bodies so we can consider an elemental mass dm in the body and find its kinetic energy.
The integrating kinetic energy of this elemental mass gives us the total kinetic energy of the body in rotational motion.
For understanding kinetic energy in rotational motion see the video – https://youtu.be/s-Cs6MuysYA