Classical Mechanics
# Rotational Kinetic Energy

A \(1.5\text{ m}\) thin rod with mass \(0.900\text{ kg}\) is standing vertically with one end on the floor. Then, if it is allowed to fall, what is the approximate speed of the other end just before it touches the floor, assuming that the gravitational acceleration is \(g=9.8\text{ m/s}^2?\)

**Note:** As shown in the figure below, the rotational inertia of a thin rod that rotates about the axis through its center perpendicular to length is \(\displaystyle I=\frac{1}{12}ML^2,\) where \(M\) and \(L\) are the mass and length of the thin rod, respectively.

A uniform thin rod with length and mass of \(7.40\text{ m}\) and \(140\text{ kg},\) respectively, is attached to a rotational axle at its one end by a single bolt. Then how much work is needed to increase the speed of the rod to \(320\text{ rev/min}\) from rest?

As shown in the figure below, the rotational inertia of a thin rod that rotates about the axis through its center perpendicular to length is \(\displaystyle I=\frac{1}{12}ML^2,\) where \(M\) and \(L\) are the mass and length of the thin rod, respectively.