Question

Angular position of a body undergoing circular motion varies with time as $\theta =2t^2+3$ radians. If radius of circular path is $1\text{m}$, the acceleration of body at $t=1\text{s}$will be

Answer 1

Answer (1)
Centripetal acceleration, $a_c={\omega }^{2}R$
$={\left(\frac{d\theta }{dt}\right)}^{2}R={\left(4t\right)}^2\left(1\right)$
Tangential acceleration
$a_T=\alpha R=\left(\frac{d^2\theta }{d{t}^2}\right)R=\left(4\right)\left(1\right)$
$a=\sqrt{a_T^2+a_C^2}$
At $t=1;a=\sqrt{4^2+{16}^2}=4\sqrt{17}{\text{m/s}}^2$