Question

A solid sphere with a moment of inertia of 2.20 kgm2 is rolling along the ground (without slipping) with an angular velocity of 15.1 rad/s . Find (a) its rotational kinetic energy and (b) its translational kinetic energy.

Answer 1

Explanation:

It is given that,

Moment of inertia of a solid sphere, $I=2.2\ kg-m^2$

Angular velocity of the solid sphere, $\omega=15.1\ rad/s$

(a) The rotational kinetic energy of the solid sphere is given by :

$K_r=\dfrac{1}{2}I\omega^2$

$K_r=\dfrac{1}{2}\times 2.2\times (15.1)^2$

$K_r=250.811\ J$

(b) The translational kinetic energy of the solid sphere is given by :

$K_t=\dfrac{1}{2}mv^2$

Moment of inertia of solid sphere is :

$I=\dfrac{2}{5}mr^2$

$K_t=\dfrac{1}{2}m(r \omega)^2$

$K_t=\dfrac{5 I\omega^2}{4}$

$K_t=\dfrac{5 \times 2.2\times (15.1)^2}{4}$

$K_t=627.02\ J$

Hence, this is required solution.