Questions $13-16$

A string is wound around the rim of a uniform disk that is pivoted to rotate without friction about a fixed axis through its center. The mass of the disk is $m=3kg$ and its radius is $R=20cm.$ The string is initially at rest and is pulled with a time dependent force $F=F_0{t}^2$ where $F_0$ is given as $10\frac{N}{s^2}.$

$13.$ What is the moment of inertia of this disk in $kg*m^2?$

$($a$)0\mathrm{.}48$

$($b$)0\mathrm{.}12$

$($c$)0\mathrm{.}03$

$($d$)0\mathrm{.}06$

$($e$)0\mathrm{.}24$

$14.$ What is the magnitude and direction of torque on the disk at $t=2s?$

$($a$)8N*m,+x$

$($b$)16N*m,-z$

$($c$)16N*m,+y$

$($d$)8N*m,-x$

$($e$)16N*m,+z$

$15.$ What is the magnitude and direction of angular acceleration of the disk at $t=2s?$

$($a$)\frac{800}{3}ra\frac{d}{s^2},-z$

$($b$)\frac{400}{3}ra\frac{d}{s^2},+x$

$($c$)\frac{800}{3}ra\frac{d}{s^2},+y$

$($d$)\frac{400}{3}ra\frac{d}{s^2},-x$

$($e$)\frac{800}{3}ra\frac{d}{s^2},+z$

$16.$ What is the magnitude and direction of the angular velocity of the disk at $t=2s?$

$($a$)400ra\frac{d}{s},-x$

$($b$)\frac{800}{9}ra\frac{d}{s},-x$

$($c$)800ra\frac{d}{s},+z$

$($d$)800ra\frac{d}{s},-z$

$($e$)800ra\frac{d}{s},+y$