Question

A solid cylinder of mass $20\text{kg}$ rotates about its axis with an angular speed of $100\text{rad/s}$. The radius of the cylinder is $0.25\text{m}$. The kinetic energy associated with the rotation of the cylinder is

• A. $3125\text{J}$
• B. $725\text{J}$
• C. $31.25\text{J}$
• D. $7.25\text{J}$

Answer 1

The correct option is A $3125\text{J}$

Given, $M=20\text{kg}$
$\omega =100\text{rad/s}$
$R=0.25\text{m}$
Moment of inertia of the solid cylinder about its axis of symmetry
$I=\frac{1}{2}M{R}^2=\frac{1}{2}\times 20\times (0.25{)}^2$
$=10\times 0.0625=0.625{\text{kg m}}^2$
Kinetic energy associated with the rotation of the cylinder is given by
$KE=\frac{1}{2}I{\omega }^2$
$=\frac{1}{2}\times 0.625\times (100{)}^2$
$=0.3125\times 10000$
$=3125\text{J}$