Classical Mechanics
# Rotational Kinetic Energy

Two identical particles each of mass \(m=10\text{ kg}\) and two thin rods are in a line, connected to each other as shown in the figure above. The two particles and two rods rotate about the rotational axis \(O\) with an angular speed of \(\omega=1\text{ rad/s}.\) If the two rods have mass and length of \((2M=4\text{ kg}, 2d=100\text{ cm})\) and \((M=2\text{ kg}, d=50\text{ cm}),\) respectively, what is the (approximate) kinetic energy of the system?

As shown in the figure below, the rotational inertia of a thin rod that rotates about 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 thin \(0.4\text{ kg}\) rod of length \(0.70\text{ m}\) hangs from the ceiling, as shown in the figure above. If the rod is pulled to one side and let go, it swings like a pendulum and passes through its lowest position with an angular speed of \(4\text{ rad/s}.\) Then what is the rod's approximate kinetic energy at its lowest position? (Neglect friction and air resistance.)

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.

×

Problem Loading...

Note Loading...

Set Loading...