1. The problem statement, all variables and given/known data
A solid cylinder of mass m and radius R has a string wound around it (basically a yoyo). A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Δt and its center of mass doesn’t move. The tension in the string is T and the rotational inertia of the cylinder about its axis is 1/2 * mR2
23) The net force on the cylinder during the time interval Δt is:
A) T B) mg C) T – mgR D) mgR – T E) zero
24) The linear acceleration of the person’s hand during the time interval Δt is:
A) (T – mg) / m B) 2g C) g/2 D) T/m E) zero
2. Relevant equations
torque = F x R = Iα = (1/2 * mR2) α
3. The attempt at a solution
I drew a free-body diagram. The yoyo has mg pulling downward at it’s axis (which is its center of mass). The yoyo also has a force F pulling up at its side, creating a torque FR.
I suppose if it’s stationary, the net force is 0. But how on earth can it be stationary? This brings me to the crux of the problem. I can’t understand how this phenomenon works.
I’ve tried with a yoyo. It’s true, if I pull up with a certain acceleration, the yoyo will be stationary for a second. However, this doesn’t make sense. I provide a torque on its side, but I do nothing to cancel out the force gravity has on it’s center. How does it stay stationary?
Also, I did not attempt 24 because I did not understand 23.
Thanks for any help.