While the CD in the figure is rotating at 7200 rev/min at t=0, it is decelerating with a constant angular acceleration. If the CD stopped in 6 seconds,

Question

While the CD in the figure is rotating at 7200 rev/min at t=0, it is decelerating with a constant angular acceleration. If the CD stopped in 6 seconds, (a) how many rad/s² is its angular acceleration? What is the (b) tangential and (c) radial acceleration of point A at t=3 s, in m/s²? (Radius of the CD is 6.5 cm.)

Answer 1

(a) ω = ω₀ + εt; ω = 0; ω₀ = 7200·2π/60 = 240π rad/s; t = 6 s; ε = (0 - 240π)/6 = - 40π rad/s² = -125.67 s^-2.

(b) tangential accelaration a_t = εr = - 125.67·0.06 m/s² = - 7.55 m/s²

(c) at t = 3s ω = 240π - 40π·3 = 120π rad/s = 377 rad/s

So, radial acelaration a_n = ω²r = 377²·0.06 = 8527.74 m/s².