King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 12

Rectangular Coordinates

Normal and Tangential Coordinates

Cylindrical Coordinates Resultant force components causing a particle to move with a known acceleration

Directions of Forces Wight force mg – vertical downward. Normal force N – perpendicular to the tangent of path Frictional force Ff – along the tangent in the opposite direction of motion. Acting force Fq – along q direction Fq

Free-Body Diagram r q Select the object Establish r, q coordinate system Set ar always acts in the positive r direction Assume aq acts in the positive q Set W = mg always acts in a vertical direction–downward in vertical problem neglect weight in horizontal problem Set the tangent line Set normal force FN perpendicular to tangent line Set frictional force Ff opposite to tangent Set acting force F along q direction Calculate the y angle using Calculate other angles Apply tangent F ar r y FN aq Ff mg q

(psi) y angle Establish r = f(q) i.e r = 0.5 q r = 10t2 and q = 0.5t r = 40q From geometry Defined between the extended radial line and the tangent to the curve. Positive – counterclockwise sense or in the positive direction of q. Negative – opposite direction to positive q. r and q perpendicular r 2 q q

Example 13-10 m= 2 Ib Smooth horizontal r = 10 t2 ft q = 0.5t rad F = ? at t = 1 s.

Problem 13.91

Review Example 13-11 Example 13-12

Thank you

Problem 108