13. Rotational Inertia & Energy

A small 10-kg object is connected to the right end of a thin rod of length 4 m and mass 5 kg. The rod is free to rotate about a fixed perpendicular axis on its left end, as shown below. The rod is initially held at rest, horizontally. When the rod is released, it falls, rotating about its axis, similar to a pendulum. What is the speed at the rod's center of mass when the rod is vertical? BONUS:What is object's speed when the rod is vertical?

The 5.0 kg, 60-cm-diameter disk in FIGURE P12.71 rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. What is the cylinder's angular velocity when it is directly below the axle?

In Example 11–1, the hand slowly pulls the string, causing the rotating mass (m = 0.75 kg) to gain speed. Calculate the work done by the hand.

In Example 11–1, the hand slowly pulls the string, causing the rotating mass (m = 0.75 kg) to gain speed. Check that the work–energy theorem is satisfied.

A cord connected at one end to a block which can slide on an inclined plane has its other end wrapped around a cylinder resting in a depression at the top of the plane as shown in Fig. 10–81. Determine the speed of the block after it has traveled 1.80 m along the plane, starting from rest. Assume there is no friction.