Calculate angular velocity, angular acceleration

The angular velocity of the circle is defined by the equation ω=3t²+2 rad/sec where t in sec. Determine the magnitudes of the velocity and acceleration of point B on the circle of 1m diameter when t=10 sec.

 Solution

ω = 3t²+2 rad/sec

a = dω / dt = 6t

t = 10 sec

a = 60 rad/sec²

VA = ω*R=(3*10^2+2)*0.5=151m/sec

a = 60 rad/sec²

a_t = a*R = 60*0.5 = 30m/sec²

a_w = ω²*R = 302^2*0.5 = 45.6m/sec²

a_A = SQRT(a_t²+ a_w²)