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The angular velocity of the circle is defined by the equation ω=3t^{2}+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 = 3t^{2}+2 rad/sec

a = dω / dt = 6t

t = 10 sec

a = 60 rad/sec^{2}

VA = ω*R=(3*10^2+2)*0.5=151m/sec

a = 60 rad/sec^{2}

a_{t }= a*R = 60*0.5 = 30m/sec^{2}

a_{w }= ω^{2}*R = 302^2*0.5 = 45.6m/sec^{2}

a_{A }= SQRT(a_{t}^{2}+ a_{w}^{2})

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