$($a$)$

Calculate the angular momentum $($in kg$$m$2/$s$)$ of an ice skater spinning at $6\mathrm{.}00$ rev$/$s given his moment of inertia is $0\mathrm{.}370$ kg$$m$2.$

kg$$m$2/$s

$($b$)$

He reduces his rate of spin $($his angular velocity$)$ by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia $($in kg$$m$2)$ if his angular velocity drops to $2\mathrm{.}05$ rev$/$s$.$

kg$$m$2$

$($c$)$

Suppose instead he keeps his arms in and allows friction with the ice to slow him to $3\mathrm{.}00$ rev$/$s$.$ What average torque $($in N$$m$)$ was exerted if this takes $14\mathrm{.}0$ seconds?

N$$m