Question

A circular disc of mass 2Kg and radius 10 cm rolls without slipping with a speed 2 m/s.The total kinetic energy of disc is .

Answer 1

Given,

$m=2kg$

$r=10cm=0.1m$

$v=2m/s$

Linear kinetic energy is given by

$K_l=\frac{1}{2}m{v}^2$

$K_l=\frac{1}{2}\times 2\times 2\times 2$

$K_l=4J$

Rotational energy is given by

$K_r=\frac{1}{2}I{\omega }^2$. . . . .(1)

Moment of inertia, $I=\frac{1}{2}m{r}^2$

$I=\frac{1}{2}\times 2\times 0.1\times 0.1$

$I=0.01kg{m}^2$

angular velocity, $\omega =\frac{v}{r}$

$\omega =\frac{2}{0.1}=20rad/s$

From equation (1),

$K_r=\frac{1}{2}\times 0.01\times (20{)}^2$

$K_r=2J$

The total energy,

$E_t=K_l+K_r=4+2$

$E_t=6J$