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

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Solution

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

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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=wRTherefore,w=9Answer: 9

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