A 20 kg uniform disk of radius $r=0.4$ m is subjected to a torque $M = 50$ N$\cdot$m. Determine its angular acceleration.

A uniform slender rod of mass $m=3$ kg and length $L=1.2$ m is pinned at one end $O$ and released from rest in the horizontal position. Determine the initial angular acceleration of the rod and the reaction at the pin.

A uniform solid cylinder of mass $m=20 \text{ kg}$ and radius $r=0.3 \text{ m}$ is released from rest on a rough incline making an angle $\theta = 30^\circ$ with the horizontal. Assuming the cylinder rolls without slipping, determine the acceleration of its mass center and the minimum coefficient of static friction required to prevent slipping.

A forklift carrying a heavy load accelerates forward. If the acceleration is too high, the rear wheels may lift off the ground, causing the forklift to tip over forward. Analyze the dynamics of this situation, identify the pivot point, and formulate the condition for tipping using the equations of motion for a rigid body.

When a batter hits a baseball, they feel a "sting" in their hands if the ball hits too close to the handle or the end of the bat. However, hitting the ball at the "sweet spot" minimizes this sting. Explain this phenomenon using the concepts of rigid body kinetics, center of percussion, and impulsive forces.