King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 23

Course coverage Kinematics of particle in various motion. (Chapter 12) Force and acceleration. (Chapter 13) Work and energy relations. (Chapter 14) Impulse and Momentum. (Chapter 15) Kinematics of a rigid bodies. (Chapter 16) Force and acceleration of a rigid bodies . (Chapter 17) Work and energy relations of a rigid bodies. (Chapter 18) Impulse and Momentum of a rigid bodies (Chapter 19)

Chapter 16 Planar Kinematics of a Rigid Body Objective To classify the various types of rigid-body. To investigate rigid-body translation and show how to analyze motion about a fixed axis.

Rigid-Body Motion Types of rigid body planar motion: Translation Rotational about fixed axis General plane motion

Translation Every line segment on the body remains parallel to its original direction during the motion

Rotation about fixed axis All particles of the body move along circular paths except those which lie on the axis of rotation

General plane motion Combination of translation and rotation

Example Curvilinear translation General plane motion Rectilinear translation Rotation about a fixed axis

Translation Position Velocity Acceleration All points move with same velocity and acceleration

Summary chapter 12 Time dependent acceleration Constant acceleration

Rotation About a Fixed axis For Line Angular Position ( q ) Defined by the angle q measured between a fixed reference line and r Measured in rad Angular Displacement Measured as dq Vector quantity Measured in radians or revolutions 1 rev = 2 p rad

Angular velocity (w ) “the time rate of change in the angular position” Angular acceleration “the time rate of change of the angular velocity” a = f(q)

Constant Angular Acceleration

Comparison

Motion of Point P Position : Velocity Is defined by the position vector r The arc-length is Velocity “tangent to the path”

Acceleration “rate of change in the velocity’s magnitude” “rate of change in the velocity’s direction” Direction of an is always toward O

r1 r2 r1 r2 s , v, a

Example 16-1 Rest at = 4t m/s2 w=? q=?

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