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Learning Goal: To apply the principle of work and energy to a rigid body. The principle of work and energy is used to solve kinetic problems that involve velocities, forces, moments, and displacements. For a rigid body, the principle is

`T_(1)+\sum U_(1-2)=T_(2)`

where

`T_(1)`

is the body's initial kinetic energy,

`\sum U_(1-2)`

is the work done by external forces and moments that act on the body, and

`T_(2)`

is the body's final kinetic energy. For a rigid body, the kinetic energy is broken into two components: the translational kinetic energy,

`((1)/(2))mv_(G)^(2)`

, and the rotational kinetic energy,

`((1)/(2))I_(G)\omega ^(2)`

, where

`m`

is the mass,

`v_(G)`

is the velocity of the body's center of mass

`G,I_(G)`

is the moment of inertia about the body's center of mass, and

`\omega `

is the body's angular velocity. Show work please.