Answer to Question #265774 in Physics for kar

Question

A wooden bar mass of 2 kg and length of 1.0 m, is placed vertically on the ground. If the bar is released to fall to the ground and its foot is not move, Find a) Kinetic energy when the bar hit the ground b) Speed of the end point of the bar when its hit the ground

Answer 1

a) Kinetic energy can be found from potential energy:

$$KE=PE=mgh_{\text{cm}}=mg\frac L2=9.8\text{ J}.$$

b) The moment of inertia:

$$I=\frac13 mL^2.$$

The kinetic rotational energy:

$$KE=\frac12 I\omega^2=\frac16mL^2\omega^2,\\\space\\ KE=\frac16 mL^2\bigg(\frac vL\bigg)^2=\frac16 mv^2.\\\space\\ v=\sqrt{\frac{6KE}{m}}=\sqrt{\frac{6·9.8}{2}}=5.4\text{ m/s}.$$