Answer to Question #170220 in Mechanics | Relativity for April

Question

A force of 16 N acts tangent to the edge of a solid cylinder weighing 18 N and which has a

diameter of 76 cm. Determine the kinetic energy of the cylinder after 15 s.

Answer 1

$$I\alpha=Fr\\0.5Mr^2\alpha=Fr\\4F=Md\alpha\\\\4Fg=Wd\alpha\\4(16)(9.8)=(18)(0.76)\alpha\\ \alpha=45.85\frac{rad}{s}\\K=0.5\frac{0.5Wd^2}{4g}(\alpha t)^2 \\K=\frac{(18)(0.76)^2}{16(9.8)}(45.85\cdot15)^2=31362.8\ J$$