Question

A shaft is turning at 65 rad/s at time t=0. Thereafter, its angular acceleration is given by
α = -10 rad/s² - 5t rad/s³ ,
where t is the elapsed time. (a) Find its angular speed at t=3 s. (b) How far does it turn in these 3s?

Answer 1

The initial angular speed of shaft 1s, a- 65 rad/s a) Angular acceleration is, α=-10-4.5t 10-5t dt 2 At t=0, ω=65 rad/s 65-0+0+ C C-65 Substitute 65 for C in equation - (1) 2 Att- 3 sec -10(3)-5 +65 2 45 =-30--+ 65 12.5 rad/s Hence, the angular speed is 12.5 rad/s

b) Angular displacement is, dt -10--2.5-+65t 0 =1-5(3)-0.83(3)' +65(3) = 122 rad Hence, the angular displacement is 122 rad.