King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 9

Review Chapter Introduction 12.2 Rectilinear Kinematics 12.4 General Curvilinear Motion –12.5 Rectangular components –12.6 Motion of a Projectile –12.7 Normal and Tangential –12.8 Polar and Cylindrical 12.9 Absolute Dependent Motion Analysis Relative motion of two particles

12.1 Introduction Mechanics Rigid-body Static Equilibrium body Dynamics Accelerated motion body Kinematics (Geometric aspect of motion) Kinetics (Analysis of force causing the motion) Deformable-bodyfluid

KINEMATICS OF PARTICLES Kinematics of particles Road Map Rectilinear motion Curvilinear motion x-y coord. n-t coord. r-  coord. Relative motion

Areas of mechanics (section12.1) 1)Statics (CE-201) - Concerned with body at rest 2)Dynamics -Concerned with body in motion 1.Kinematics, is a study the geometry of the motion s, v, a 2.Kinetics, is a study of forces cause the motion F, m, motion

12.2 Rectilinear Kinematics Time dependent accelerationConstant acceleration This applies to a freely falling object:

–Rectangular Components Position vector r = x i + y j + z k Velocity v = v x i + v y j + v z k (tangent to path) Acceleration a = a x i + a y j +a z k (tangent to hodograph) –Normal and Tangential Components Radius of curvature (  Velocity Acceleration –Polar & Cylindrical Components Position r = r u r Velocity Acceleration General Curvilinear Motion

a c = -g = 9.81 m/s 2 = 32.2 ft/s2 Vertical MotionHorizontal Motion 12.6 Motion of a Projectile

12.9 Absolute Dependent Motion of Two Particles –Position –Velocity –Acceleration Relative-Motion Analysis of Two Particles Using Translating Axes –Position –Velocity –Acceleration

Review problems 25 Examples 10 Homework Problems 10 Old Homework Problems 13 Problems in appendix D page 655&666 Problems included in the Lecture Notes

Continuous Motion The position of a particle is s = (0.5t 3 +4t) ft, where t is in second. Determine the velocity and the acceleration of the particle when t = 3 s.

Projectile Determine the speed at which the basketball at A must be thrown at the angle of 30 o so that it makes it to the basket at B. At what speed does it pass through the hoop? Horizontal Vertical

Normal and Tangential At a given instant, the automobile has a speed of 25 m/s and an acceleration of 3 m/s 2 acting in the direction shown. Determine the radius of curvature of the path and the rate of increase of the automobile ’ s speed.

Polar and Cylindrical The slotted fork is rotating about O at a constant rate of 3 rad/s. Determine the radial and transverse components of velocity and acceleration of the pin A at the instant  = 360 o. The path is defined by the spiral groove r = (5+  in., where  is in radians.

Dependent Motion Determine the speed of point P on the cable in order to lift the platform at 2 m/s

Relative independent motion At the instant shown, cars A and B are traveling at the speeds shown. If B is accelerating at 1200 km/h 2 while A maintains a constant speed, determine the velocity and acceleration of A with respect to B.