A solid sphere with a radius of $0\mathrm{.}22$ m and a mass of $14$ kg is initially spinning on its axis with a period of $12$ s$.$

What is the angular velocity of the sphere?

Answer Choices for Problem $6\mathrm{.}1$

$0\mathrm{.}083$ rad$/$s

$1\mathrm{.}91$ rad$/$s

$1\mathrm{.}07$ rad$/$s

$0\mathrm{.}52$ rad$/$s

None of these.

You decide to stop the sphere from spinning by placing your hand on the edge one radius away from the axis of rotation. Your hand creates a torque that slows the sphere to a stop in $15$s$.$

Which of the following is CORRECT? In all answers, the torque from your hand is the same.

Answer Choices for Problem $6\mathrm{.}2$

None of these are correct.

If the sphere had a larger radius but the same mass, it would take more time to stop.

If the sphere had less mass but the same radius, it would stop in the same amount of time.

If the sphere had more mass but the same radius, it would take less time to stop.

If the sphere had a smaller radius but the same mass, it would take more time to stop.