Having now mastered the technique of Lagrangians, this section will be one big application of the methods. Textbook Authors: Young, Hugh D.; Freedman, Roger A. , ISBN-10: 0321973615, ISBN-13: 978-0-32197-361-0, Publisher: Pearson θ π θ 2π 2 1 x r r x A A = − = − Differentiate to relate the translational and angular velocities. A) r EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today’s Objectives : Students will be able to: a) Identify support reactions, and, b) Draw a free-body diagram. All problems of rigid body dynamics, exact analytical solutions of which are known, were solved in the last century. f=120 revolution f=2 revolution/second T=1/f=1/2s b) If object starts its motion from 4: Plane Kinematics of Rigid Bodies 4.2 Rotation 4.2 Rotation Rotation of a rigid body is described by its angular motion, which is dictated by the change in the angular position (specified by angle θmeasured from any fixed line) of any line attached to the body.
For two-dimensional rigid body dynamics problems, the body experiences motion in one plane, due to forces acting in that plane.

A) are usually different B) are always the same C) depend on their position D) depend on their relative position 2. If a rigid body is in translation only, the velocity at points A and B on the rigid body _____ . Here is a quick outline of how we analyze motion of rigid bodies. This message occurs if you’ve selected Solvers > Memory Caching > Enable for a rigid body, then you change attributes on the rigid body that affect the rigid body’s translation or rotation. 1. b) Find the change in velocity vector when it rotates 600, 900 and 1800. a) 60s. 2.3 The Statics of Rigid Bodies A material body can be considered to consist of a very large number of particles. Ch. It does 120 revolutions in one minute. Chapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. 1. The Motion of Rigid Bodies Figure 22: Wolfgang Pauli and Niels Bohr stare in wonder at a spinning top. An object in horizontal rotates on a circular road with 10m/s velocity. A number of problems, which have been solved incompletely, exist. 2. As we shall see, these can often be counterintuitive. The general definition of moment of inertia, also called rotational inertia, for a rigid body is I = ∑ m i r i 2 and is measured in SI units of kilogram‐meters 2. A 100-gram ball connected to one end of a cord with a length of 30 cm.
CONDITIONS FOR RIGID-BODY EQUILIBRIUM ( Section 5.1) In contrast to the forces on a particle, the forces on a rigid-body are not usually concurrent and may cause rotation of the body (due to the moments created by the … Because the rigid body is cached, it gets the translation and rotation information for the rigid body from the cache. October 2013 with 1,927 Reads How we measure 'reads' A 'read' is counted each time someone views a … 21 21 21 21 All lines on a rigid body in its plane of motion have RIGID-BODY ROTATION: ACCELERATION OF POINT P Using the vector formulation, the acceleration of P can also be defined by differentiating the velocity. Known : The axis of rotation at AB. CONDITIONS FOR RIGID-BODY EQUILIBRIUM ( Section 5.1) In contrast to the forces on a particle, the forces on a rigid-body are not usually concurrent and may cause rotation of the body (due to the moments created by the … EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today’s Objectives : Students will be able to: a) Identify support reactions, and, b) Draw a free-body diagram. Sample Problem 15.2 x y SOLUTION: • The displacement of the gear center in one revolution is equal to the outer circumference. Rotational Motion Exam2 and Problem Solutions 1. The moment of inertia of the particle. You won’t see any effect on the rigid body until you delete the cache.


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