The 12-kg rod A B is pinned to the 40-kg disk. If the disk is given an angular velocity ωD=100 r

step 1 Since friction is internal between rod and disc and no external torques act horizontally, angula

The 12-kg rod A B is pinned to the 40-kg disk. If the disk...

The $12-\mathrm{kg} \operatorname{rod} A B$ is pinned to the $40-\mathrm{kg}$ disk. If the disk is given an angular velocity $\omega_{D}=100 \mathrm{rad} / \mathrm{s}$ while the rod is held stationary, and the assembly is then released, determine the angular velocity of the rod after the disk has stopped spinning relative to the rod due to frictional resistance at the bearing $B .$ Motion is in the horizontal plane. Neglect friction at the pin $A$.

Key Concepts

Conservation of Angular Momentum

This concept states that if no external torques act on a system, the total angular momentum remains constant. In problems involving rotating bodies that interact through friction or collisions, it is used to relate the initial and final angular velocities of the components, even if energy is dissipated in the process.

Moment of Inertia

The moment of inertia quantifies how the mass of an object is distributed with respect to an axis of rotation. It plays a key role in determining the angular acceleration and the overall dynamics of rotating systems. Different shapes and mass distributions require calculating separate moments of inertia to predict rotational behavior accurately.

Rotational Coupled Dynamics

In systems where multiple bodies are connected or interact—such as when friction couples the rotation of a disk and a rod—their individual rotational motions influence one another. Understanding how angular momenta are exchanged between parts helps in analyzing the resulting common rotational speeds once frictional or internal torques have acted.

Frictional Torque and Energy Dissipation

Friction at the interface between rotating components generates a torque that can transfer angular momentum between system parts while dissipating energy as heat. Although energy is not conserved in these interactions due to the losses from friction, the overall angular momentum remains constant if no external torques are applied.

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