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# (Solved): Learning Goal: To apply the principle of work and energy to a rigid body. The principle of work and ...

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.

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