Question

One end of a thin rod is attached to a pivot about which it can rotate without friction. Air resistance is absent. The rod has a length of 0.48 m and is uniform. It is hanging vertically straight downward. The end of the rod nearest the floor is given a linear speed V so that the rod begins to rotate upward about the pivot. What must be the value of V such that the rod comes to a momentary halt in a straight up orientation, exactly opposite to its initial orientation?

Answer 1

5.32 m/s

Explanation:

We can determine the velocity from the following equation (initial kinetic energy:

`(1)/(6)\cdot v^2_0=g\cdot L`

Where L is the length of the rod and g would be gravity, we replace and calculate the value of the initial velocity:

`\begin{gathered} v^2_0=6\cdot9.81\cdot0.48 \\ v^{}_0=\sqrt[]{28.2528} \\ v_0=5.32\text{ m/s} \end{gathered}`

The velocity is 5.32 m/s