A lathe, initially at rest, accelerates at .60 rad/s^2 for 10s, then runs at a constant angular velocity for 20s, and finally decelerates uniformly for 10s to come to a complete stop. What is its average angular velocity?

Answer 1

V1 = a*t1 = 0.6rad/s^2 * 10s. = 6 rad/s.
d1 = 0.5a*t1^2 = 0.3*10^2 = 30 Radians.

d2=V1*t2 = 6rad/s. * 20s. = 120 Rad1ans

V2 = V1 + a*t3 = 0
6 + a*10 = 0
10a = -6
a = -0.60 m/s^2

V2^2 = V1^2 + 2a*d = 0
d2 = -(V1^2)/2a = -(6^2)/-1.2 = 30 Rad.

V=(d1+d2)/(t1+t2+t3)=(120+30)/(10+20+10)
= 3.75 Rad/s.=Average angular velocity.