Chapt.10RotationofaRigidObjectAboutaFixedAxis10.1.PDFVIP

Chapt. 10 Rotation of a Rigid Object About a Fixed Axis 10.1 Angular Position, Velocity, and Acceleration Translation: motion along a straight line (circular motion ?) Rotation: surround itself, spins rigid body: no elastic, no relative motion rotation: moving surrounding the fixed axis, rotation axis, axis of rotation s 360 Angular position: θ = , 1rev = 360o = 2π (rad ) , 1rad = 57=.3 o r 2π Angular displacement: ∆θ = θ1 − θ2 An angular displacement in the counterclockwise direction is positive θ − θ ∆θ 2 1 Angular velocity: averaged ω = = t − t ∆t 2 1 dθ instantaneous: ω = , rpm = rev per minute dt ∆ω Angular acceleration: averaged α = ∆t dω instantaneous: α = dt Sample Problem: The disk in Fig. 11-5a is rotating about its central axis like a merry-go-round. The angular position θ(t) of a reference line on the disk is given by θ= − 1.00 −0.600 t +0.250 t2 with t in seconds, q in radians, and the zero angular position as indicated in the figure. a) Graph the angular position of the disk versus time from t = -3.0 s to t = 6.0 s. Sketch the disk and its angular position reference line at t = -2.0 s, 0 s, and 4.0 s, and when the curve crosses the t axis. b) At what time tmin does θ(t) reach the minimum value? What is that minimum value? c) Graph the angular velocity ω of the disk versus time from t = -3.0 s to t = 6.0 s. Sketch the disk and indicate the direction of turning and th