[Music] thank you hi students welcome to 4G silver Academy Tamil in the episode derivation parallel axis theorem parallel Axis or a rigid body in the rigid body cooler particle Circle okay particles so in the water particle Mass small m a portum total mass capital M is the center of gravity for gravitation force one day it is center of gravity or equal a distance smaller sorry theorem so in the parallel axis so first is center of gravity of a rigid body of mass m either rigid body in the rigid body layer the G the center of gravity is a total mass capital M a b axis is parallel to c d axis next a and another distance between the axis the Ada on the rundax is distance foreign proof so in The Parallax is gonna answer the final equation moment of inertia at a B axis equal to moment of inertia at the CD axis that means center of gravity level plus total mass of the rigid body under distance between the two axis other s Square so you run the parallel axis first step foreign on the gravitational force on the center of gravity left moment of inertia formula Mass into distance Square in the point length in the gravity can a mass Circle small number distance R square then a moment of inertia number total moment of inertia that means moment of inertia of foreign total moment of inertia for a rigid body or a rigid body artist CD and the CD access only a summation whatever is summation summation is the first equation organize the first equation for next second equation moment of inertia number series if a moment of inertia is so moment of inertia moment of inertia and the particles at a b a b yeah yum yum distance in the axis foreign foreign [Music] a square plus 2 a b 2 a b plus b square if in the formula foreign total moment of inertia total moment of inertia for a rigid body rigid body at a yeah at a B okay foreign meaning I is equal to summation m R square plus 2 r a plus a square so in the equation the second equation in the equation the second equation part the Step n upon a foreign summation M into two R A summation m 2 R A Plus summation M into a square summation m a square okay next step I is equal to summation m r Square the summation is summation m r a is foreign Center of on the rigid body layer now look at total value okay therefore Finance I is equal to ig plus m a square proof on H is summation m aterial to a equal to zero silence foreign Central Arkansas therefore I is equal to ig plus m a square parallel axis is the equation of parallel axis theorem is the equation of parallel axis theorem so definition you know diagram the derivation is foreign