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Conservation of Energy with Rotation definitions

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  • Rotational Kinetic Energy
    Energy due to an object's rotation, calculated as 1/2 I omega^2, where I is moment of inertia and omega is angular velocity.
  • Linear Kinetic Energy
    Energy due to an object's linear motion, calculated as 1/2 m v^2, where m is mass and v is velocity.
  • Moment of Inertia
    Resistance of an object to changes in its rotational motion, for a solid disc I = 1/2 M R^2.
  • Angular Velocity
    Rate of change of angular position of a rotating body, often denoted by omega.
  • Conservation of Energy
    Principle stating total energy remains constant in an isolated system, accounting for kinetic and potential energies.
  • Non-conservative Work
    Work done by forces like friction or external forces, not stored as potential energy.
  • Perpendicular Axis
    An axis at a 90-degree angle to the plane of rotation, around which an object spins.
  • Solid Disc
    A circular object with uniform mass distribution, used in rotational dynamics problems.
  • Unwinding
    Process where a cable or rope is pulled off a rotating object, affecting its angular velocity.
  • Without Slipping
    Condition where there is no relative motion between surfaces in contact, allowing v = R * omega.
  • Potential Energy
    Energy stored due to an object's position or configuration, often related to height in gravitational fields.
  • Radius
    Distance from the center to the edge of a circle or disc, crucial in calculating moment of inertia.
  • Force
    An influence that causes an object to undergo a change in motion, measured in newtons.
  • Joules
    Unit of energy in the International System of Units, used to measure work or energy.
  • Radians per Second
    Unit of angular velocity, describing how fast an object rotates or revolves relative to another point.