Just as objects in motion tend to stay in motion, objects that are spinning tend to keep spinning! This concept is known as angular momentum.
When Jared spins the bike wheel, it rotates around the center axis. Once the bike wheel is spinning, it becomes more difficult to rotate the bike wheel, because it already has angular momentum. Jared has to apply a torque in order to rotate the bike wheel.
Then, Jared uses a motor to spin up the bike wheel, and he sits on a stool. The bike wheel has angular momentum because it is spinning. Just as linear momentum is conserved for a whole system, angular momentum is also conserved. So when Jared turns the spinning bike wheel, his body starts spinning in the opposite direction!
Next, Jared spins while holding dumbbells! We observe that when the dumbbells are far from the center, they have to go around in big circles. When they are near the center, the same amount of angular momentum makes Jared spin faster!
This concept of how spread out the mass is from the center is called the moment of inertia. Just like linear momentum depends on an object’s mass and its velocity, angular momentum depends on its moment of inertia and angular velocity. When Jared pulls the dumbbells in, his moment of inertia decreases. Because angular momentum stays the same, his angular velocity increases and he spins faster.