Rotational motion of a cylinder

Calculate the kinetic energy of a cylindrical body of radius r= 0.08 meter and mass m= 1.5kg at time t= 5 s, if this body rotates around an axis passing through the center of the cylinder with a constant acceleration Ԑ= 5 rad/s², if at time t=.

Correct answer:

E =  1.5 J

Step-by-step explanation:

$$\begin{gathered} r=0.08\text{m} \\ m=1.5\text{kg} \\ t=5\text{s} \\ Ԑ=5{\text{rad/s}}^2 \\ \omega =Ԑ\cdot t=5\cdot 5=25\text{rad/s} \\ I=\frac{1}{2}\cdot m\cdot r^2=\frac{1}{2}\cdot 1.5\cdot 0.08^2=\frac{3}{625}=0.0048{\text{kgm}}^2 \\ E=\frac{1}{2}\cdot I\cdot {\omega }^2=\frac{1}{2}\cdot 0.0048\cdot 25^2=1.5\text{J} \end{gathered}$$

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