Chapter 2 – kinematics of particles Tuesday, September 8, 2015: Class Lecture 6 Today’s Objective: Polar Coordinates Relative motion – Translating Axes

Relative Motion For two particles with independent motion, use a 2 nd frame and origin. We will focus first only on the situations where the second frame has translation, and no rotation. Absolute position of each particle is r A and r B measured from the common origin O. The origin of the second frame is x’, y’, z’ is attached to A and moves with A. The axes of frame x’, y’, z’ are allowed to Translate only, without any rotation. With this Stipulation, all rigid bodies can be treated as a Particle.

Relative Motion If we observing from point B and Study motion of A w.r.t. B

Relative Motion Observing from point A: In the sketch, reverse the direction of the vectors. The fixed frame (the origin) can be chosen arbitrarily.

Problem 2/183 Car A rounds a curve of 150-m radius at a constant speed of 54-km/h. At the instant represented, car B is moving at 81 km/h but is slowing down at the rate 3 m/s 2 Determine the velocity and acceleration of car A as observed from car B.

Problem 2/185 pp 92 Given: V B = 800 km/h V A = 1200 km/h Required: V A/B