Chapter 2 – kinematics of particles
Thursday, September 3, 2015
Today’s Objective:
Curvilinear motion
Polar Coordinates
Polar Coordinates
• Time derivatives of the unit vectors
As done before in the case of the derivative of unit vector et the derivative of unit
vectors er and eϴ can be found.
Circular Motion
• The Polar coordinates and the n-t
coordinates are the same for a
circular motion.
• t-direction is same as the 𝜃 direction
and n-direction is same as rdirection.
Cylindrical Coordinates
• Cylindrical Coordinates: r, 𝜃, 𝑧
Velocity
Acceleration
Example of r-𝜃 Coordinates
• Problem 2.145
Given: Constant speed, h = 10 km,
d𝜃/𝑑𝑡 = -0.020 rad/s
Req: v and d2r/dt2 at 𝜃 = 600
Vector Notations
• Rectangular Coordinates: x, y, z
Example of r-𝜃 Coordinates
Problem 2.161
Given: d𝛽/𝑑𝑡 = 60 rad/s
Required: for 𝛽 = 300 find, dr/dt, d2r/dt, d𝜃/dt, and d2𝜃/d2t
Polar Coordinates
• Spherical Coordinates: R,𝜃,∅
Problem 2/177 pp 86
Given: d𝜃/𝑑𝑡 = Ω = 10 𝑑𝑒𝑔/𝑠, 𝑑∅/𝑑𝑡 = 7 deg/s, voA = .5 m/s,
Required: at ∅ = 30 deg, OA = 9 m, AB = 6 m. Find v and a of end B