# Physics C Mechanics: torque on a yoyo

**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 * mR^{2}

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 * mR^{2}) 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.

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