Question $2$

The figure on the left shows the overhead view of a small coin $($can be considered as a point$)$ on top of a

circular table of radius $R=0\mathrm{.}5$ meter. The coin is at a distance of $r=0\mathrm{.}35$ meter from the center of the

circular table. The table rotates with an angular acceleration of $=2trad{s}^{-2}.$ Initially $($at time $t=0),$

the table had an angular speed of $5rad{s}^{-1}$ clockwise and had an initial angular position of $60$ with respect

to a reference line. $($Interpret clockwise speed as negative and anti$-$clockwise speed as positive.$)$ The figure

on the right shows a small puck of mass $m=500$ grams rotating on a frictionless table. It is connected to

an ideal rope that passes through a hole and is connected to a cylinder of mass $M=2kg.$ Here $r$ is $0\mathrm{.}1$

meter.

$($a$)$ Calculate the angular speed and angular position of the coin with respect to the reference line as a

function of time and hence at time $t=4$ second.

$($b$)$ Does the coin change it's direction or rotation at some time? If yes, when? Calculate the number of

complete rotations that the coin complete up to that time.

$($c$)$ Calculate the angular speed of the puck for which the cylinder does not fall downwards. $($Hint: The

tension force will provide necessary centripetal acceleration here.$)$