![]() ![]() If more than three unknowns exist in the equations, we will sometimes have to go back to kinematics to relate quantities such as acceleration and angular acceleration. Plugging the known forces, moments, and accelerations into the above equations, we can solve for up to three unknowns. problems for rigid bodies requires that we introduce and define angular- velocity and angular-acceleration vectors for the. Additionally, it's important to always use the center of mass for the accelerations in our force equations and take the moments and moment of inertia about the center of mass for our moment equation. ![]() Since this is a rigid body system, we include both the translational and rotational versions.Īs we did with the previous translational systems, we will break the force equation into components, turning the one vector equation into two scalar equations. In this chapter and in Chapters 17 and 18, we will be concerned with the kinetics of rigid bodies, i.e., relations between the forces acting on a rigid body. ![]() At its core, this means going back to Newton's Second Law. 4 F G ma 3 F G The two equations for the motion of a system of particles apply to the most general case of the motion of a rigid body. SP5/6 Motion of the equilateral triangular plate ABC in its plane is controlled by the hydraulic cylinder D. Next, we move on to identifying the equations of motion. It is also sometimes helpful to label any key dimensions as well as using dashed lines to identify any known accelerations or angular accelerations. Be sure to identify the center of mass, as well as identifying all known and unknown forces, and known and unknown moments acting on the body. Those are solutions subject to certain conditions on the position and angular velocity, not only on the integrals of motion. To analyze a body undergoing general planar motion, we will start by drawing a free body diagram of the body in motion. The tire is both translating and rotating as it is pushed along. Contents Introduction Principle of Work and Energy for a Rigid Body Work of Forces Acting on a Rigid Body Kinetic Energy of a Rigid Body in Plane Motion Systems of Rigid Bodies Conservation of Energy Power Sample Problem 17.1 Sample Problem 17.2 Sample Problem 17.3 Sample Problem 17.4 Sample Problem 17.5 Principle of Impulse and Momentum. \): This tire being rolled along the ground is an example of general planar motion. Problems involving eccentric impact are solved by supplementing the principle of impulse and momentum with the application of the coefficient of restitution. ![]()
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