Kinetics (continued) Rotation of a Rigid Body in the x-y plane
Euler’s second law governs the rotational acceleration (angular acceleration) of a rigid body subjected to external moments. The moment of the external forces acting on the rigid body results in a change in the angular momentum of the rigid body. In general the angular momentum, HC, of a rigid body about its center of mass is given by HC = ICω, where IC is
the moment of inertia of mass of the body about its mass center and ω is its angular velocity. Consider a rigid body of mass, m, located at its center of mass, C. Then the expression for Euler’s second Law in mass center form is
where Σ MC is the sum of the moments of the external forces acting on the rigid body about its mass center and dHC/dt is the rate of change of the angular momentum (in the inertial frame) of the rigid body about its center of mass. In general dHC/dt = IC α + ω x (ICω) Here IC is the moment of inertia of mass about the mass center, α and ω are the angular acceleration and angular velocity measured with respect to a fixed frame of reference. For planar kinetics ω x (ICω) = 0. The result for planar motion is
that the angular acceleration is governed by:
Again two classes of problems exist. The first is to determine the angular acceleration of the center of mass of the body resulting from the moment of external forces acting on the body. In this type you must first identify the external moments acting on the body by constructing a “free body diagram”. The second type is to determine the external moments acting on the body resulting from its angular acceleration. |
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