1. King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 6

2. Objective To investigate particle motion along a curved path “ Curvilinear Motion ” using three coordinate systems –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 Position (particle itself) Velocity v =  u t (tangent to path) Acceleration (normal & tangent) –Polar & Cylindrical Components

3. Curvilinear Motion: Cylindrical Components Section 12.8 Rotated object-guided track problem Cylindrical component Polar component “ plane motion ”

4. Application: Rotated object-guided track problem

5. Polar Coordinates Radial coordinate r Transverse coordinate  and r are perpendicular Theta  in radians 1 rad = 180 o /  Direction u r and u 

6. Position Position vector r = r u r

7. Velocity Instantaneous velocity = time derivative of r r = r u r Where

8. Velocity (con.) Magnitude of velocity Angular velocity Tangent to the path Angle = 

9. Acceleration Instantaneous acceleration = time derivative of v

10. Acceleration (con.) Angular acceleration Magnitude Direction “ Not tangent ” Angle 

11. Cylindrical Coordinates For spiral motion cylindrical coordinates is used r, , and z. Position Velocity Acceleration

12. Time Derivative to evaluate If r = r(t) and  t) If r = f(  use chain rule

13. Review Example 12.18 Example 12.20