Example $9\mathrm{.}1$

The angular position $$ of a $0\mathrm{.}36$ m diameter flywheel is given by

$=(2\mathrm{.}0)t^3$

a$)$ Find $,$ in radians and in degrees, at $t_1=2\mathrm{.}0s$ and $t_2=5\mathrm{.}0s.$

b$)$ Find the distance that a particle on the flywheel rim moves over the time interval from $t_1=2\mathrm{.}0s$ to $t_2=5\mathrm{.}0s.$

c$)$ Find the average angular velocity in rev$/$min over that time interval.

d$)$ Find the instantaneous angular velocity at $t_1=2\mathrm{.}0s$ and $t_2=5\mathrm{.}0s.$