Question 5The chef at a pizza restaurant tosses a spinning disk of pizza dough into the air. As the disk stretches outward in midair and its diameter increases, what happens to the disk's angular momentum and angular velocity about the disk's center of mass? [Note that the disk's weight, which acts at the disk's center of gravity, produces zero torque on the disk about the disk's center of mass. Ignore any effects due to the air.]1 pointThe disk's angular velocity is constant, but the disk's angular momentum increases.The disk's angular momentum is constant, but the disk's angular velocity increases.The disk's angular momentum is constant, but the disk's angular velocity decreases.The disk's angular momentum and angular velocity are both constant.
Question
Question 5The chef at a pizza restaurant tosses a spinning disk of pizza dough into the air. As the disk stretches outward in midair and its diameter increases, what happens to the disk's angular momentum and angular velocity about the disk's center of mass? [Note that the disk's weight, which acts at the disk's center of gravity, produces zero torque on the disk about the disk's center of mass. Ignore any effects due to the air.]1 pointThe disk's angular velocity is constant, but the disk's angular momentum increases.The disk's angular momentum is constant, but the disk's angular velocity increases.The disk's angular momentum is constant, but the disk's angular velocity decreases.The disk's angular momentum and angular velocity are both constant.
Solution
The correct answer is "The disk's angular momentum is constant, but the disk's angular velocity decreases."
Here's why:
Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω). It can be represented by the equation L = Iω.
When the chef tosses the spinning disk of pizza dough into the air, the dough stretches and its diameter increases. This means the moment of inertia (I) of the dough increases because the mass of the dough is now distributed further from the center of mass.
According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless acted on by an external torque. In this case, we're told to ignore any effects due to the air and that the disk's weight produces zero torque. This means there's no external torque acting on the dough, so its angular momentum remains constant.
However, because the moment of inertia (I) has increased and the angular momentum (L) is constant, the angular velocity (ω) must decrease to maintain the equation L = Iω.
So, as the disk of pizza dough stretches outward in midair and its diameter increases, its angular momentum remains constant, but its angular velocity decreases.
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