For this part, imagine that the string is wound around the center axle of a yo-yo; the axle radius is Raxle, but the yo-yo casing has a radius Rcasing≫Raxle and moment of inertia I≫mr2axle. In the limit the moment of inertia of the yo-yo I→∞ and the mass m of the yo-yo remains finite, what magnitudes would you expect for the tension T in the vertical section of string and the downward acceleration a of the center of mass?
Choose the option that best describes the limiting values of T and a under the conditions given.
Choose the option that best describes the limiting values of and under the conditions given.
A T=0 and a=0
B T=∞ and a=0
C T=mg and a=0
D T=∞ and a=g
E T=0 and a=∞
F T=∞ and a=∞
It's neither D, B, nor E
I'm very confused. If Inertia goes to infinity, then kinetic energy must go to infinity right? But if kinetic energy goes to infinity, tension goes to infinity thus the yo-yo flies upwards, right? And if tension is 0, a has to be infinite?
Best Answer
It is C. As I→∞ the yo-yo becomes increasingly unresponsive (has a smaller angular acceleration) to any applied torque; it will seem like it cannot begin rotating. If it can't rotate, the string can't unwind, so the center of mass can't fall, and the net force on the yo-yo must be zero.