IGNORE PROBLEM 5..... A disk begins to rotate about an axis through its center with constant angular acceleration alpha = 0.50 rad/s2 starting from rest at time t = 0. Determine the following: (a) the number of revolutions the disk rotates through before it attains angular velocity omega = 45rpm, (b) the angular velocity of the disk (report your answer in both rad/s and rpm) at time t = 5s, and (c) the speed and the magnitude o'the acceleration of point P at t = 6s. The disk in problem 4 begins to rotate about an axis through its center with constant angular acceleration alpha = 0.02t3 rad/s2
Explanation / Answer
Given At t =0, ?i = 0 Angular acceleration,a = 0.5 rad/s^2 ? = 45 rpm = 45 *0.1047 rad/s = 4.7 rad/s a)?^2 - ?i^2 = 2a? (4.7 rad/s)^2 = 2 * 0.5 rad/s^2 *? ? = 22.09 rad = (22.09 /2p) rev ? = 3.51 rev ------------------------------------------------------------------ b)At t =5s, the angular velocity ? is ? = a t = 0.5 rad/s^2 *5s ? = 2.5 rad/s In terms of rpm ? = 2.5 *(60/2p) rpm = 23.87 rpm ------------------------------------------------------------------------------- c)The speed at t = 6s v = r? Given r = 100mm = 0.1 m where ? = at = 0.5 rad/s^2 *6s = 3 rad/s v = 0.1 m * 3rad/s v = 0.3 m/s Acceleration ,a = v^2/r = (0.3 m/s)^2/0.1 m a = 0.9 m/s^2