Given data
*The given mass of the solid cylinder is m = 0.274 kg
*The given radius of the cylinder is r = 2.00 cm = 0.02 m
*The given speed is v = 5.00 cm/s = 0.05 m/s
The formula for the total kinetic energy is given as
[tex]\begin{gathered} U_T=U_k+U_R \\ U_T=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2 \\ =\frac{1}{2}mv^2+\frac{1}{2}(\frac{1}{2}mr^2)(\frac{v}{r})^2 \end{gathered}[/tex]*Here U_K is the translation kinetic energy
*Here U_R is the rotational kinetic energy
*Here 'I' is the moment of inertia of the solid cylinder
Substitute the known values in the above expression as
[tex]\begin{gathered} U_T=\frac{1}{2}(0.274)(0.05)^2+\frac{1}{2}(\frac{1}{2}\times0.274\times(0.02)^2)(\frac{0.05}{0.02})^2 \\ =0.000342+0.000171 \\ =5.13\times10^{-4}\text{ J} \\ =5.13\times10^{-1}\text{ mJ} \end{gathered}[/tex]Hence, the total kinetic energy is U_T = 5.13 × 10^-1 mJ
