Transcript ME101 Lecture 6

Chapter 2 – kinematics of particles
Tuesday, September 8, 2015: Class Lecture 6
Today’s Objective:
• Polar Coordinates
• Relative motion – Translating Axes
Example of r-𝜃 Coordinates
Problem 2.161
Given: d𝛽/𝑑𝑡 = 60 rad/s cw
Required: for 𝛽 = 300 find, dr/dt, d2r/dt, d𝜃/dt, and d2𝜃/d2t
Relative Motion
• For two particles with independent motion, use a 2nd 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 rA and rB
• 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/s2 Determine the velocity and acceleration of car A as observed from car
B.
Problem 2/185 pp 92
Given: VB = 800 km/h
VA = 1200 km/h
Required: VA/B