SEHS$3302$ Assignment $1($due date Sept $302024,23$:$59)$

$(15$ marks$)$

The angular acceleration of the disk is defined by $=3t^2+12ra\frac{d}{s},$ where $t$ is in

seconds. If the disk is originally rotating at ${}_0=12ra\frac{d}{s},$ determine the magnitude of

the velocity and the $n$ and $t$ components of acceleration of point $B$ on the disk when

$t=2s.$ Indicate the direction of the acceleration components on the diagram.

Analysis: Different from the class notes, here, the acceleration is a function of time. By

substituting $t=2$ into the expression you can find the angular acceleration at $2$ s $.$ The

key part is how to find the ${|}_t||=2s,$ you need to use ${\displaystyle \underset{0}{\overset{t}{}}}dt=-{}_0.$ Because $$ is not

a constant, you cannot use $={}_0+t.$