Question

Acceleration of the particle at $t=0.5$ second and 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 $0.5s$ is given as,

$a_1=\frac{v^2}{r}$

$a_1=\frac{{\left(2t\right)}^2}{r}$

$a_1=\frac{{\left(2\times 0.5\right)}^2}{1}$

$a_1=1m/s^2$

The acceleration at $3s$ is given as,

$a_2=\frac{v^2}{r}$

$a_2=\frac{{\left(2t\right)}^2}{r}$

$a_2=\frac{{\left(2\times 3\right)}^2}{1}$

$a_2=36m/s^2$