Rotational motion of a cylinder

Calculate the kinetic energy of a cylindrical body with radius r = 0.08 m and mass m = 1.5 kg at time t = 5 s, given that the body rotates about an axis through the centre of the cylinder with a constant angular acceleration ε = 5 rad/s², starting from rest at t = 0 s.

Final 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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