Question

A uniform disc is spun with an angular velocity $\overrightarrow{\omega }$ and simultaneously projected with a linear velocity $v$ towards left on a plank, while the plank moves towards right with a constant velocity $2v$. If the disc rolls without sliding on the plank just after its spinning, find the magnitude of $\overrightarrow{\omega }$ in rad/sec. (Take $v=3m$ $s^{-1}$, $R=1m$)

Answer 1

velocity of the disc w.r.t the plank is $3v$.
For the disc to roll purely just as it lands on the plank,
$3v=wR$
Therefore,
$w=9$
Answer: 9