Polar cylindrical and spherical co ordinates Tutorial 4

#EngineeringDynamics #EngineeringMechanics #Mechanics #Dynamics #Kinematics #CurvilinearMotion #CoordinateSystems #PolarCoordinates #CylindricalCoordinates #SphericalCoordinates #PolarKinematics #CylindricalKinematics #SphericalKinematics #PositionVector #VelocityVector #AccelerationVector #UnitVectors #Radial #Transverse #AngularMotion #AngularVelocity #AngularAcceleration #RotationalKinematics #3DMotion #ParticleKinematics #VectorCalculus #MotionAnalysis #ClassicalMechanics #AppliedMechanics #MechanicalEngineering ► Watch AD-FREE video AND download practice questions (COMPLETELY FREE) here: https://www.pemtutoring.co.uk/courses/04-polar-cylindrical-and-spherical-coordinates/ (no login or sign up required) ► FREE downloadable resources here: https://www.pemtutoring.co.uk/engineering-dynamics/ (no login or sign up required) 👇 SUBSCRIBE to PEM TUTORING YouTube channel 👇 https://www.youtube.com/channel/UCPm2FuKmrjLmbG0HbnV-mfg?sub_confirmation=1 ★☆★ FOLLOW ON SOCIAL MEDIA ★☆★ YouTube: https://www.youtube.com/channel/UCPm2FuKmrjLmbG0HbnV-mfg Website: https://www.pemtutoring.co.uk/ Instagram: https://www.instagram.com/pemtutoring/ Facebook: https://www.facebook.com/pages/category/Product-Service/PEM-Tutoring-101112152080368/ In this lesson we explore alternative coordinate systems used to describe curvilinear motion in Engineering Dynamics / Engineering Mechanics. You’ll learn how to set up polar, cylindrical, and spherical coordinates, and how to obtain the key kinematics results for position, velocity, and acceleration (including unit vectors and full derivations). ⏱️ TIMESTAMPS ⏱️ 00:00 Introduction 00:27 Polar co-ordinates 04:03 Polar co-ordinates – position 04:29 Polar co-ordinates – velocity (Full Derivation) 08:47 Polar co-ordinates – acceleration (Full Derivation) 10:34 Polar co-ordinates summary 12:47 Visualisation of polar co-ordinates 19:57 EXAMPLE: Polar co-ordinates 23:48 Cylindrical co-ordinates 27:18 EXAMPLE: Cylindrical co-ordinates (Tricky) 33:30 Spherical co-ordinates 35:50 Spherical co-ordinates (Derivation of unit vectors) 48:15 Spherical co-ordinates – velocity (Full Derivation) 54:04 Spherical co-ordinates – acceleration (Full Derivation) 59:50 Spherical co-ordinates equations summary 01:00:06 EXAMPLE: Spherical co-ordinates (Very Tricky)