Final answer:
Without sufficient information on the moment of inertia or initial angular velocity, we cannot calculate the new angular velocity when the angle of the yoyo is reduced to half. Angular velocity increases under the conservation of angular momentum when the angle decreases, assuming no external torques are applied.
Step-by-step explanation:
The student is asking about the change in angular velocity of a yoyo when the angle it creates with the vertical is reduced to half of its initial value. Although the provided information is not sufficient to calculate the new angular velocity directly, I'll explain the concept using the rotational dynamics.
Angular velocity (ω) relates to the rate at which an object rotates or revolves relative to another point, expressed in radians per second (rad/s). When the angle is halved, assuming there are no external torques and that angular momentum is conserved, the angular velocity would increase due to the conservation of angular momentum (L = Iω, where L is angular momentum and I is the moment of inertia).
Using the information from a related scenario in the question, if we know the initial angular velocity and the moments of inertia before and after the change in angle, we could apply the conservation of angular momentum to find the new angular velocity:
ωinitial × Iinitial = ωfinal × Ifinal
However, without the moments of inertia or the initial angular velocity, we cannot complete this calculation.