Question

Angular displacement at $t=3sec.$

Answer 1

The final speed is given as,

${\omega }_2=\frac{480}{\pi }rpm$

${\omega }_2=16rad/sec$

The angular acceleration is given as,

$\alpha =\frac{{\omega }_2-{\omega }_1}{t}$

$\alpha =\frac{16-12}{2}$

$\alpha =2rad/s^2$

The velocity is given as,

$v=r\alpha t$

$v=1\times 2\times t$

$v=2tm/s$

The acceleration at $3s$ is given as,

$a=\frac{v^2}{r}$

$a=\frac{{\left(2t\right)}^2}{r}$

$a=\frac{{\left(2\times 3\right)}^2}{1}$

$a=36m/s^2$

The displacement is given as,

$s=ut+\frac{1}{2}a{t}^2$

$s=16\times 3+\frac{1}{2}\times 36{\left(3\right)}^2$

$s=210$

The angular displacement is given as,

$\theta =\frac{s}{r}$

$\theta =\frac{210}{1}$

$\theta ={210}^{\circ }$

The angular displacement is ${210}^{\circ }$.